Confluent Hypergeometric Functions - 13.9 Zeros
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 13.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \ceiling{-a}}
p(a,b) = \ceiling{-a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a < 0, b \geq 0} | p(a , b) = ceil(- a)
|
p[a , b] == Ceiling[- a]
|
Failure | Failure | Failed [90 / 90] Result: (.8660254040+.5000000000*I)*(-1.500000000, 1.500000000)-2.
Test Values: {a = -3/2, b = 3/2, p = 1/2*3^(1/2)+1/2*I}
Result: (-.5000000000+.8660254040*I)*(-1.500000000, 1.500000000)-2.
Test Values: {a = -3/2, b = 3/2, p = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Error |
| 13.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = 0}
p(a,b) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \geq 0, b \geq 0} | p(a , b) = 0 |
p[a , b] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 13.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = 1}
p(a,b) = 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \geq 0, -1 < b, b < 0} | p(a , b) = 1 |
p[a , b] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 13.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \floor{-\tfrac{1}{2}b}-\floor{-\tfrac{1}{2}(b+1)}}
p(a,b) = \floor{-\tfrac{1}{2}b}-\floor{-\tfrac{1}{2}(b+1)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a \geq 0, b \leq -1} | p(a , b) = floor(-(1)/(2)*b)- floor(-(1)/(2)*(b + 1))
|
p[a , b] == Floor[-Divide[1,2]*b]- Floor[-Divide[1,2]*(b + 1)]
|
Failure | Failure | Error | Error |
| 13.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \ceiling{-a}-\ceiling{-b}}
p(a,b) = \ceiling{-a}-\ceiling{-b} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ceiling{-a} \geq \ceiling{-b}, a < 0, b < 0} | p(a , b) = ceil(- a)- ceil(- b)
|
p[a , b] == Ceiling[- a]- Ceiling[- b]
|
Failure | Failure | Error | Error |
| 13.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(a,b) = \floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}+1\right)}-\floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}\right)}}
p(a,b) = \floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}+1\right)}-\floor{\tfrac{1}{2}\left(\ceiling{-b}-\ceiling{-a}\right)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ceiling{-b} > \ceiling{-a}, \ceiling{-a} > 0} | p(a , b) = floor((1)/(2)*(ceil(- b)- ceil(- a)+ 1))- floor((1)/(2)*(ceil(- b)- ceil(- a)))
|
p[a , b] == Floor[Divide[1,2]*(Ceiling[- b]- Ceiling[- a]+ 1)]- Floor[Divide[1,2]*(Ceiling[- b]- Ceiling[- a])]
|
Failure | Failure | Failed [20 / 20] Result: (.8660254040+.5000000000*I)*(-.5000000000, -1.500000000)-1.
Test Values: {a = -1/2, b = -3/2, p = 1/2*3^(1/2)+1/2*I}
Result: (-.5000000000+.8660254040*I)*(-.5000000000, -1.500000000)-1.
Test Values: {a = -1/2, b = -3/2, p = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Error |
| 13.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle T(a,b) = \floor{-a}+1}
T(a,b) = \floor{-a}+1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a < 0, \EulerGamma@{a}\EulerGamma@{a-b+1} > 0} | T(a , b) = floor(- a)+ 1
|
T[a , b] == Floor[- a]+ 1
|
Failure | Failure | Error | Error |
| 13.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle T(a,b) = \floor{-a}}
T(a,b) = \floor{-a} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a < 0, \EulerGamma@{a}\EulerGamma@{a-b+1} < 0} | T(a , b) = floor(- a)
|
T[a , b] == Floor[- a]
|
Failure | Failure | Error | Error |
| 13.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle T(a,b) = 0}
T(a,b) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a > 0} | T(a , b) = 0 |
T[a , b] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 13.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(a,b) = \ceiling{b-a-1}}
P(a,b) = \ceiling{b-a-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a+1 < b} | P(a , b) = ceil(b - a - 1)
|
P[a , b] == Ceiling[b - a - 1]
|
Failure | Failure | Failed [100 / 100] Result: (.8660254040+.5000000000*I)*(-1.500000000, 1.500000000)-2.
Test Values: {P = 1/2*3^(1/2)+1/2*I, a = -3/2, b = 3/2}
Result: (.8660254040+.5000000000*I)*(-1.500000000, .5000000000)-1.
Test Values: {P = 1/2*3^(1/2)+1/2*I, a = -3/2, b = 1/2}
... skip entries to safe data |
Error |
| 13.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(a,b) = 0}
P(a,b) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a+1 \geq b} | P(a , b) = 0 |
P[a , b] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |