Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7795)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-11/4

http://functions.wolfram.com/07.22.03.7795.01

Input Form

HypergeometricPFQ[{6}, {-(11/4), 15/4}, -z] == (1/(3932160 z^(11/4))) (-12 z^(3/4) (1091475 - 680400 z + 49360 z^2 + 190976 z^3 + 28672 z^4) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-(-9823275 + 22963500 z - 15271200 z^2 + 3084480 z^3 + 4515840 z^4 + 704512 z^5)) Cos[2 Sqrt[z]] + 2 Sqrt[z] (9823275 - 9865800 z + 5609520 z^2 + 2217600 z^3 - 368640 z^4 + 32768 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (9823275 - 9865800 z + 5609520 z^2 + 2217600 z^3 - 368640 z^4 + 32768 z^5) Cos[2 Sqrt[z]] + (-9823275 + 22963500 z - 15271200 z^2 + 3084480 z^3 + 4515840 z^4 + 704512 z^5) 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]