Numerical Methods - 3.10 Continued Fractions
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| 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 | - | - |