Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7655)

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=23/4

http://functions.wolfram.com/07.22.03.7655.01

Input Form

HypergeometricPFQ[{5}, {23/4, 25/4}, -z] == -((1/(4294967296 z^(21/4))) (4583103525 (6 z^(1/4) (-3315 + 176 z) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((9945 - 7200 z + 256 z^2) Cos[2 Sqrt[z]] + 32 (405 - 64 z) Sqrt[z] Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (32 Sqrt[z] (-405 + 64 z) Cos[2 Sqrt[z]] + (9945 - 7200 z + 256 z^2) Sin[2 Sqrt[z]]))))

Standard Form

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MathML Form

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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]