Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6809)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-23/4

http://functions.wolfram.com/07.22.03.6809.01

Input Form

HypergeometricPFQ[{3}, {-(23/4), 23/4}, -z] == (1/(188416 z^(19/4))) (4 z^(3/4) (-756212081625 + 182451168900 z - 18378360000 z^2 + 838918080 z^3 - 17295104 z^4 + 115712 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (7 (324090892125 - 633777744600 z + 187459272000 z^2 - 19620057600 z^3 + 917579520 z^4 - 19261440 z^5 + 131072 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (2268636244875 - 1411595885700 z + 236713276800 z^2 - 16337280960 z^3 + 518918400 z^4 - 6702080 z^5 + 16384 z^6) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (2268636244875 - 1411595885700 z + 236713276800 z^2 - 16337280960 z^3 + 518918400 z^4 - 6702080 z^5 + 16384 z^6) Cos[2 Sqrt[z]] - 7 (324090892125 - 633777744600 z + 187459272000 z^2 - 19620057600 z^3 + 917579520 z^4 - 19261440 z^5 + 131072 z^6) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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/> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 633777744600 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 324090892125 </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> </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]