Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9538)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9538.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(15/4)}, z] == (1/(2238484248000 z^(5/2))) ((-1031198293125 + 1031198293125 E^(4 Sqrt[z]) - 2062396586250 Sqrt[z] - 2062396586250 E^(4 Sqrt[z]) Sqrt[z] - 1264936572900 z + 1264936572900 E^(4 Sqrt[z]) z + 219988969200 z^(3/2) + 219988969200 E^(4 Sqrt[z]) z^(3/2) - 41902660800 z^2 + 41902660800 E^(4 Sqrt[z]) z^2 + 8821612800 z^(5/2) + 8821612800 E^(4 Sqrt[z]) z^(5/2) - 2075673600 z^3 + 2075673600 E^(4 Sqrt[z]) z^3 + 553512960 z^(7/2) + 553512960 E^(4 Sqrt[z]) z^(7/2) - 170311680 z^4 + 170311680 E^(4 Sqrt[z]) z^4 + 61931520 z^(9/2) + 61931520 E^(4 Sqrt[z]) z^(9/2) - 27525120 z^5 + 27525120 E^(4 Sqrt[z]) z^5 + 15728640 z^(11/2) + 15728640 E^(4 Sqrt[z]) z^(11/2) - 12582912 z^6 + 12582912 E^(4 Sqrt[z]) z^6 + 16777216 z^(13/2) + 16777216 E^(4 Sqrt[z]) z^(13/2) - 67108864 z^7 + 67108864 E^(4 Sqrt[z]) z^7 - 67108864 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) Erf[Sqrt[2] z^(1/4)] - 67108864 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 1031198293125 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> </mrow> <mo> - </mo> <mn> 1031198293125 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 19 <sep /> 4 </cn> </apply> </list> <list> <cn type='rational'> 7 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2238484248000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> 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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]