Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7369)

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/07.22.03.7369.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), -(17/4)}, -z] == (1/45176306175) (45176306175 - 9243234000 z + 1796256000 z^2 - 496742400 z^3 + 289013760 z^4 - 1189085184 z^5 - 1105960960 z^6 + 18481152 z^7 - 2048 Sqrt[Pi] z^(21/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((885225 + 1133088 z - 18176 z^2) Cos[2 Sqrt[z]] + 2 Sqrt[z] (885225 - 112672 z + 256 z^2) Sin[2 Sqrt[z]]) - 2048 Sqrt[Pi] z^(21/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (885225 - 112672 z + 256 z^2) Cos[2 Sqrt[z]] + (-885225 - 1133088 z + 18176 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]