Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1282)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=5/2

http://functions.wolfram.com/07.22.03.1282.01

Input Form

HypergeometricPFQ[{-(7/2)}, {5/2, 11/2}, -z] == (1/(10485760 z^(9/2))) (3 (2 Sqrt[z] (-165375 - 78750 z - 160650 z^2 + 312060 z^3 + 334790 z^4 + 38652 z^5 + 1116 z^6 + 8 z^7) Cos[2 Sqrt[z]] + (165375 - 141750 z - 3150 z^2 + 128940 z^3 + 301770 z^4 + 37580 z^5 + 1108 z^6 + 8 z^7) Sin[2 Sqrt[z]] + 32 z^3 (-22050 + 55125 z + 44100 z^2 + 4900 z^3 + 140 z^4 + z^5) SinIntegral[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]