Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9458)

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`=3/2

http://functions.wolfram.com/07.22.03.9458.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, 1/4}, z] == (1/(320785920 Sqrt[z])) ((4 (-6320160 + 27457920 Sqrt[z] - 197890560 z - 50414175 z^(3/2) + 226095660 z^2 + 9399600 z^(5/2) - 38770368 z^3 - 404736 z^(7/2) + 1631232 z^4 + 4096 z^(9/2) - 16384 z^5 + E^(4 Sqrt[z]) (6320160 + 27457920 Sqrt[z] + 197890560 z - 50414175 z^(3/2) - 226095660 z^2 + 9399600 z^(5/2) + 38770368 z^3 - 404736 z^(7/2) - 1631232 z^4 + 4096 z^(9/2) + 16384 z^5)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-916620705 + 931170240 z - 156280320 z^2 + 6537216 z^3 - 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-916620705 + 931170240 z - 156280320 z^2 + 6537216 z^3 - 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 197890560 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 27457920 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 6320160 </cn> </apply> </apply> <cn type='integer'> -6320160 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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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]