Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9366)

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`=-1/2

http://functions.wolfram.com/07.22.03.9366.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), 5/4}, z] == (1/(1150156800 z^(1/4))) ((-4 z^(1/4) (-28229175 - 133485300 Sqrt[z] - 229919040 z + 1117355520 z^(3/2) + 80862720 z^2 - 337766400 z^(5/2) - 4997120 z^3 + 20185088 z^(7/2) + 65536 z^4 - 262144 z^(9/2) + E^(4 Sqrt[z]) (-28229175 + 133485300 Sqrt[z] - 229919040 z - 1117355520 z^(3/2) + 80862720 z^2 + 337766400 z^(5/2) - 4997120 z^3 - 20185088 z^(7/2) + 65536 z^4 + 262144 z^(9/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (115540425 + 1027026000 z - 4694976000 z^2 + 1365811200 z^3 - 80936960 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (115540425 + 1027026000 z - 4694976000 z^2 + 1365811200 z^3 - 80936960 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1027026000 </cn> <ci> z </ci> </apply> <cn type='integer'> 115540425 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </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]