Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7555)

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=-5/4

http://functions.wolfram.com/07.22.03.7555.01

Input Form

HypergeometricPFQ[{5}, {-(5/4), 21/4}, -z] == -((1/(4194304 z^(17/4))) (663 (2 z^(1/4) (6081075 - 2687580 z + 574560 z^2 - 73920 z^3 + 11264 z^4) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-6081075 + 12417300 z - 4586400 z^2 + 759360 z^3 - 92160 z^4 + 16384 z^5) Cos[2 Sqrt[z]] - 10 Sqrt[z] (1216215 - 861840 z + 200592 z^2 - 26112 z^3 + 4096 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (10 Sqrt[z] (1216215 - 861840 z + 200592 z^2 - 26112 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + (-6081075 + 12417300 z - 4586400 z^2 + 759360 z^3 - 92160 z^4 + 16384 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]