Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7451)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-17/4

http://functions.wolfram.com/07.22.03.7451.01

Input Form

HypergeometricPFQ[{5}, {-(17/4), 17/4}, -z] == (1/(3342336 z^(13/4))) (6 z^(1/4) (91216125 - 45945900 z + 12141360 z^2 - 2862976 z^3 + 441600 z^4 + 12288 z^5) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-273648375 + 575675100 z - 243991440 z^2 + 57214080 z^3 - 14657280 z^4 + 811008 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 2 Sqrt[z] (273648375 - 210810600 z + 60207840 z^2 - 14826240 z^3 + 2568192 z^4 + 65536 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (273648375 - 210810600 z + 60207840 z^2 - 14826240 z^3 + 2568192 z^4 + 65536 z^5) Cos[2 Sqrt[z]] + (-273648375 + 575675100 z - 243991440 z^2 + 57214080 z^3 - 14657280 z^4 + 811008 z^5 + 65536 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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<cn type='integer'> 243991440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 575675100 </cn> <ci> z </ci> </apply> <cn type='integer'> -273648375 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </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]