Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7473)

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=-15/4

http://functions.wolfram.com/07.22.03.7473.01

Input Form

HypergeometricPFQ[{5}, {-(15/4), 23/4}, -z] == (1/(6291456 z^(19/4))) (19 (4 z^(3/4) (-39800635875 + 11683772100 z - 1545944400 z^2 + 115758720 z^3 - 5788416 z^4 + 176128 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (21 (5685805125 - 11416204800 z + 3881077200 z^2 - 537926400 z^3 + 41160960 z^4 - 2088960 z^5 + 65536 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (119401907625 - 80537757300 z + 16572956400 z^2 - 1661869440 z^3 + 101525760 z^4 - 4300800 z^5 + 65536 z^6) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (119401907625 - 80537757300 z + 16572956400 z^2 - 1661869440 z^3 + 101525760 z^4 - 4300800 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 21 (5685805125 - 11416204800 z + 3881077200 z^2 - 537926400 z^3 + 41160960 z^4 - 2088960 z^5 + 65536 z^6) Sin[2 Sqrt[z]])))

Standard Form

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MathML Form

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</apply> <apply> <times /> <cn type='integer'> 3881077200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11416204800 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 5685805125 </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> </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]