3.10: Difference between revisions

Latest revision as of 11:04, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
3.10#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = u_{0}} `b_{0} = u_{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	b[0] = u[0]	Subscript[b, 0] == Subscript[u, 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = 1} `b_{1} = 1`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	b[1] = 1	Subscript[b, 1] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = u_{1}} `a_{1} = u_{1}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[1] = u[1]	Subscript[a, 1] == Subscript[u, 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = 1+\frac{u_{n}}{u_{n-1}}} `b_{n} = 1+\frac{u_{n}}{u_{n-1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	b[n] = 1 +(u[n])/(u[n - 1])	Subscript[b, n] == 1 +Divide[Subscript[u, n],Subscript[u, n - 1]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = -\frac{u_{n}}{u_{n-1}}} `a_{n} = -\frac{u_{n}}{u_{n-1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n \geq 2}	a[n] = -(u[n])/(u[n - 1])	Subscript[a, n] == -Divide[Subscript[u, n],Subscript[u, n - 1]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e_{0}^{n} = 0} `e_{0}^{n} = 0`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(exp(1)[0])^(n) = 0	(Subscript[E, 0])^(n) == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{1}^{n} = c_{n+1}/c_{n}} `q_{1}^{n} = c_{n+1}/c_{n}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(q[1])^(n) = c[n + 1]/c[n]	(Subscript[q, 1])^(n) == Subscript[c, n + 1]/Subscript[c, n]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}} `e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j \geq 1, k \geq 0}	(exp(1)[j])^(k) = (exp(1)[j - 1])^(k + 1)+ (q[j])^(k + 1)- (q[j])^(k)	(Subscript[E, j])^(k) == (Subscript[E, j - 1])^(k + 1)+ (Subscript[q, j])^(k + 1)- (Subscript[q, j])^(k)	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}} `q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j \geq 1, k \geq 0}	(q[j + 1])^(k) = (q[j])^(k + 1)*(exp(1)[j])^(k + 1)/(exp(1)[j])^(k)	(Subscript[q, j + 1])^(k) == (Subscript[q, j])^(k + 1)*(Subscript[E, j])^(k + 1)/(Subscript[E, j])^(k)	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex10	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{0} = c_{0}} `a_{0} = c_{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[0] = c[0]	Subscript[a, 0] == Subscript[c, 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex11	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{1} = q_{1}^{0}} `a_{1} = q_{1}^{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[1] = (q[1])^(0)	Subscript[a, 1] == (Subscript[q, 1])^(0)	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex12	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{2} = e_{1}^{0}} `a_{2} = e_{1}^{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[2] = (exp(1)[1])^(0)	Subscript[a, 2] == (Subscript[E, 1])^(0)	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3} = q_{2}^{0}} `a_{3} = q_{2}^{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[3] = (q[2])^(0)	Subscript[a, 3] == (Subscript[q, 2])^(0)	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{4} = e_{2}^{0}} `a_{4} = e_{2}^{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	a[4] = (exp(1)[2])^(0)	Subscript[a, 4] == (Subscript[E, 2])^(0)	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{n} = b_{n}} `u_{n} = b_{n}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	u[n] = b[n]	Subscript[u, n] == Subscript[b, n]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}} `u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = n-1}	u[k] = b[k]+(a[k + 1])/(u[k + 1])	Subscript[u, k] == Subscript[b, k]+Divide[Subscript[a, k + 1],Subscript[u, k + 1]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10.E14	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C = \sum_{k=0}^{\infty}t_{k}} `C = \sum_{k=0}^{\infty}t_{k}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} \neq 0}	(b[0]+(a[1])/(b[1]+(a[2])/(b[2]+ ..))) = sum(t[k], k = 0..infinity)	(Subscript[b, 0]+Divide[Subscript[a, 1],Subscript[b, 1]+Divide[Subscript[a, 2],Subscript[b, 2]+ \[Ellipsis]]]) == Sum[Subscript[t, k], {k, 0, Infinity}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex18	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{0} = a_{0}} `t_{0} = a_{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	t[0] = a[0]	Subscript[t, 0] == Subscript[a, 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex19	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{k} = \rho_{k}t_{k-1}} `t_{k} = \rho_{k}t_{k-1}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	t[k] = rho[k]*t[k - 1]	Subscript[t, k] == Subscript[\[Rho], k]*Subscript[t, k - 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex20	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{0} = 0} `\rho_{0} = 0`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	rho[0] = 0	Subscript[\[Rho], 0] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex21	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}} `\rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	rho[k] = (a[k](1 + rho[k - 1]))/(1 - a[k](1 + rho[k - 1]))	Subscript[\[Rho], k] == Divide[Subscript[a, k](1 + Subscript[\[Rho], k - 1]),1 - Subscript[a, k](1 + Subscript[\[Rho], k - 1])]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex22	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{0} = b_{0}} `C_{0} = b_{0}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	C[0] = b[0]	Subscript[C, 0] == Subscript[b, 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex23	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{1} = 1/b_{1}} `D_{1} = 1/b_{1}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	D[1] = 1/b[1]	Subscript[D, 1] == 1/Subscript[b, 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.10#Ex26	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}} `D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	D[n] = (1)/(D[n - 1]*a[n]+ b[n])	Subscript[D, n] == Divide[1,Subscript[D, n - 1]*Subscript[a, n]+ Subscript[b, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-

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+{{DISPLAYTITLE:Numerical Methods - 3.10 Continued Fractions}}
 <div style="width: 100%; height: 75vh; overflow: auto;">
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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex1 3.10#Ex1] || [[Item:Q1409|<math>b_{0} = u_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{0} = u_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[0] = u[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 0] == Subscript[u, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex1 3.10#Ex1] || <math qid="Q1409">b_{0} = u_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{0} = u_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[0] = u[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 0] == Subscript[u, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex2 3.10#Ex2] || [[Item:Q1410|<math>b_{1} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{1} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[1] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 1] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex2 3.10#Ex2] || <math qid="Q1410">b_{1} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{1} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[1] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 1] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex3 3.10#Ex3] || [[Item:Q1411|<math>a_{1} = u_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = u_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = u[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == Subscript[u, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex3 3.10#Ex3] || <math qid="Q1411">a_{1} = u_{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = u_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = u[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == Subscript[u, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex4 3.10#Ex4] || [[Item:Q1412|<math>b_{n} = 1+\frac{u_{n}}{u_{n-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{n} = 1+\frac{u_{n}}{u_{n-1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[n] = 1 +(u[n])/(u[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, n] == 1 +Divide[Subscript[u, n],Subscript[u, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex4 3.10#Ex4] || <math qid="Q1412">b_{n} = 1+\frac{u_{n}}{u_{n-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{n} = 1+\frac{u_{n}}{u_{n-1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[n] = 1 +(u[n])/(u[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, n] == 1 +Divide[Subscript[u, n],Subscript[u, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex5 3.10#Ex5] || [[Item:Q1413|<math>a_{n} = -\frac{u_{n}}{u_{n-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n} = -\frac{u_{n}}{u_{n-1}}</syntaxhighlight> || <math>n \geq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n] = -(u[n])/(u[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n] == -Divide[Subscript[u, n],Subscript[u, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex5 3.10#Ex5] || <math qid="Q1413">a_{n} = -\frac{u_{n}}{u_{n-1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{n} = -\frac{u_{n}}{u_{n-1}}</syntaxhighlight> || <math>n \geq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[n] = -(u[n])/(u[n - 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, n] == -Divide[Subscript[u, n],Subscript[u, n - 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex6 3.10#Ex6] || [[Item:Q1416|<math>e_{0}^{n} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e_{0}^{n} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(exp(1)[0])^(n) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[E, 0])^(n) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex6 3.10#Ex6] || <math qid="Q1416">e_{0}^{n} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e_{0}^{n} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(exp(1)[0])^(n) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[E, 0])^(n) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex7 3.10#Ex7] || [[Item:Q1417|<math>q_{1}^{n} = c_{n+1}/c_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q_{1}^{n} = c_{n+1}/c_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(q[1])^(n) = c[n + 1]/c[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[q, 1])^(n) == Subscript[c, n + 1]/Subscript[c, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex7 3.10#Ex7] || <math qid="Q1417">q_{1}^{n} = c_{n+1}/c_{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q_{1}^{n} = c_{n+1}/c_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(q[1])^(n) = c[n + 1]/c[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[q, 1])^(n) == Subscript[c, n + 1]/Subscript[c, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex8 3.10#Ex8] || [[Item:Q1418|<math>e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}</syntaxhighlight> || <math>j \geq 1, k \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(exp(1)[j])^(k) = (exp(1)[j - 1])^(k + 1)+ (q[j])^(k + 1)- (q[j])^(k)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[E, j])^(k) == (Subscript[E, j - 1])^(k + 1)+ (Subscript[q, j])^(k + 1)- (Subscript[q, j])^(k)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex8 3.10#Ex8] || <math qid="Q1418">e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>e_{j}^{k} = e_{j-1}^{k+1}+q_{j}^{k+1}-q_{j}^{k}</syntaxhighlight> || <math>j \geq 1, k \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(exp(1)[j])^(k) = (exp(1)[j - 1])^(k + 1)+ (q[j])^(k + 1)- (q[j])^(k)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[E, j])^(k) == (Subscript[E, j - 1])^(k + 1)+ (Subscript[q, j])^(k + 1)- (Subscript[q, j])^(k)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex9 3.10#Ex9] || [[Item:Q1419|<math>q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}</syntaxhighlight> || <math>j \geq 1, k \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(q[j + 1])^(k) = (q[j])^(k + 1)*(exp(1)[j])^(k + 1)/(exp(1)[j])^(k)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[q, j + 1])^(k) == (Subscript[q, j])^(k + 1)*(Subscript[E, j])^(k + 1)/(Subscript[E, j])^(k)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex9 3.10#Ex9] || <math qid="Q1419">q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q_{j+1}^{k} = q_{j}^{k+1}e_{j}^{k+1}/e_{j}^{k}</syntaxhighlight> || <math>j \geq 1, k \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(q[j + 1])^(k) = (q[j])^(k + 1)*(exp(1)[j])^(k + 1)/(exp(1)[j])^(k)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[q, j + 1])^(k) == (Subscript[q, j])^(k + 1)*(Subscript[E, j])^(k + 1)/(Subscript[E, j])^(k)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex10 3.10#Ex10] || [[Item:Q1420|<math>a_{0} = c_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{0} = c_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[0] = c[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 0] == Subscript[c, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex10 3.10#Ex10] || <math qid="Q1420">a_{0} = c_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{0} = c_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[0] = c[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 0] == Subscript[c, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex11 3.10#Ex11] || [[Item:Q1421|<math>a_{1} = q_{1}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = q_{1}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = (q[1])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == (Subscript[q, 1])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex11 3.10#Ex11] || <math qid="Q1421">a_{1} = q_{1}^{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{1} = q_{1}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[1] = (q[1])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 1] == (Subscript[q, 1])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex12 3.10#Ex12] || [[Item:Q1422|<math>a_{2} = e_{1}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{2} = e_{1}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[2] = (exp(1)[1])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 2] == (Subscript[E, 1])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex12 3.10#Ex12] || <math qid="Q1422">a_{2} = e_{1}^{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{2} = e_{1}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[2] = (exp(1)[1])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 2] == (Subscript[E, 1])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex13 3.10#Ex13] || [[Item:Q1423|<math>a_{3} = q_{2}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{3} = q_{2}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[3] = (q[2])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 3] == (Subscript[q, 2])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex13 3.10#Ex13] || <math qid="Q1423">a_{3} = q_{2}^{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{3} = q_{2}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[3] = (q[2])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 3] == (Subscript[q, 2])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex14 3.10#Ex14] || [[Item:Q1424|<math>a_{4} = e_{2}^{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{4} = e_{2}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[4] = (exp(1)[2])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 4] == (Subscript[E, 2])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex14 3.10#Ex14] || <math qid="Q1424">a_{4} = e_{2}^{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{4} = e_{2}^{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[4] = (exp(1)[2])^(0)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, 4] == (Subscript[E, 2])^(0)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex16 3.10#Ex16] || [[Item:Q1427|<math>u_{n} = b_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{n} = b_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[n] = b[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, n] == Subscript[b, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex16 3.10#Ex16] || <math qid="Q1427">u_{n} = b_{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{n} = b_{n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[n] = b[n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, n] == Subscript[b, n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex17 3.10#Ex17] || [[Item:Q1428|<math>u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}</syntaxhighlight> || <math>k = n-1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[k] = b[k]+(a[k + 1])/(u[k + 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, k] == Subscript[b, k]+Divide[Subscript[a, k + 1],Subscript[u, k + 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex17 3.10#Ex17] || <math qid="Q1428">u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>u_{k} = b_{k}+\frac{a_{k+1}}{u_{k+1}}</syntaxhighlight> || <math>k = n-1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">u[k] = b[k]+(a[k + 1])/(u[k + 1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[u, k] == Subscript[b, k]+Divide[Subscript[a, k + 1],Subscript[u, k + 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10.E14 3.10.E14] || [[Item:Q1430|<math>C = \sum_{k=0}^{\infty}t_{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C = \sum_{k=0}^{\infty}t_{k}</syntaxhighlight> || <math>a_{n} \neq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(b[0]+(a[1])/(b[1]+(a[2])/(b[2]+ ..))) = sum(t[k], k = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[b, 0]+Divide[Subscript[a, 1],Subscript[b, 1]+Divide[Subscript[a, 2],Subscript[b, 2]+ \[Ellipsis]]]) == Sum[Subscript[t, k], {k, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10.E14 3.10.E14] || <math qid="Q1430">C = \sum_{k=0}^{\infty}t_{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C = \sum_{k=0}^{\infty}t_{k}</syntaxhighlight> || <math>a_{n} \neq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(b[0]+(a[1])/(b[1]+(a[2])/(b[2]+ ..))) = sum(t[k], k = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[b, 0]+Divide[Subscript[a, 1],Subscript[b, 1]+Divide[Subscript[a, 2],Subscript[b, 2]+ \[Ellipsis]]]) == Sum[Subscript[t, k], {k, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex18 3.10#Ex18] || [[Item:Q1431|<math>t_{0} = a_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{0} = a_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[0] = a[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, 0] == Subscript[a, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex18 3.10#Ex18] || <math qid="Q1431">t_{0} = a_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{0} = a_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[0] = a[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, 0] == Subscript[a, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex19 3.10#Ex19] || [[Item:Q1432|<math>t_{k} = \rho_{k}t_{k-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{k} = \rho_{k}t_{k-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[k] = rho[k]*t[k - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, k] == Subscript[\[Rho], k]*Subscript[t, k - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex19 3.10#Ex19] || <math qid="Q1432">t_{k} = \rho_{k}t_{k-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>t_{k} = \rho_{k}t_{k-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">t[k] = rho[k]*t[k - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[t, k] == Subscript[\[Rho], k]*Subscript[t, k - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex20 3.10#Ex20] || [[Item:Q1433|<math>\rho_{0} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho_{0} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho[0] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Rho], 0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex20 3.10#Ex20] || <math qid="Q1433">\rho_{0} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho_{0} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho[0] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Rho], 0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex21 3.10#Ex21] || [[Item:Q1434|<math>\rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho[k] = (a[k]*(1 + rho[k - 1]))/(1 - a[k]*(1 + rho[k - 1]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Rho], k] == Divide[Subscript[a, k]*(1 + Subscript[\[Rho], k - 1]),1 - Subscript[a, k]*(1 + Subscript[\[Rho], k - 1])]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex21 3.10#Ex21] || <math qid="Q1434">\rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho_{k} = \frac{a_{k}(1+\rho_{k-1})}{1-a_{k}(1+\rho_{k-1})}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho[k] = (a[k]*(1 + rho[k - 1]))/(1 - a[k]*(1 + rho[k - 1]))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Rho], k] == Divide[Subscript[a, k]*(1 + Subscript[\[Rho], k - 1]),1 - Subscript[a, k]*(1 + Subscript[\[Rho], k - 1])]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex22 3.10#Ex22] || [[Item:Q1435|<math>C_{0} = b_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{0} = b_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[0] = b[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, 0] == Subscript[b, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex22 3.10#Ex22] || <math qid="Q1435">C_{0} = b_{0}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>C_{0} = b_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">C[0] = b[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[C, 0] == Subscript[b, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex23 3.10#Ex23] || [[Item:Q1436|<math>D_{1} = 1/b_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{1} = 1/b_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[1] = 1/b[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, 1] == 1/Subscript[b, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex23 3.10#Ex23] || <math qid="Q1436">D_{1} = 1/b_{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{1} = 1/b_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[1] = 1/b[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, 1] == 1/Subscript[b, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.10#Ex26 3.10#Ex26] || [[Item:Q1439|<math>D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[n] = (1)/(D[n - 1]*a[n]+ b[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, n] == Divide[1,Subscript[D, n - 1]*Subscript[a, n]+ Subscript[b, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.10#Ex26 3.10#Ex26] || <math qid="Q1439">D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>D_{n} = \frac{1}{D_{n-1}a_{n}+b_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">D[n] = (1)/(D[n - 1]*a[n]+ b[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[D, n] == Divide[1,Subscript[D, n - 1]*Subscript[a, n]+ Subscript[b, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |}
 </div>

3.10: Difference between revisions

Latest revision as of 11:04, 28 June 2021

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