Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acty)

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.acty.01

Input Form

HypergeometricPFQ[{7/4}, {-(11/2), 23/4}, z] == (1/(154618822656 z^(19/4))) ((19 (4 z^(1/4) (8754746870244375 + 11672995826992500 Sqrt[z] + 8655099344892000 z + 4425163574832000 z^(3/2) + 1669667634835200 z^2 + 481750235366400 z^(5/2) + 108287675596800 z^3 + 18997837824000 z^(7/2) + 2554331136000 z^4 + 251456913408 z^(9/2) + 16374562816 z^5 + 536870912 z^(11/2) + E^(4 Sqrt[z]) (-8754746870244375 + 11672995826992500 Sqrt[z] - 8655099344892000 z + 4425163574832000 z^(3/2) - 1669667634835200 z^2 + 481750235366400 z^(5/2) - 108287675596800 z^3 + 18997837824000 z^(7/2) - 2554331136000 z^4 + 251456913408 z^(9/2) - 16374562816 z^5 + 536870912 z^(11/2))) + 151412625 E^(2 Sqrt[z]) Sqrt[2 Pi] (-57820455 + 4512816 z - 177408 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] - 151412625 E^(2 Sqrt[z]) Sqrt[2 Pi] (-57820455 + 4512816 z - 177408 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 177408 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4512816 </cn> <ci> z </ci> </apply> <cn type='integer'> -57820455 </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> </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]