Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0620)

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=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=7/2

http://functions.wolfram.com/07.22.03.0620.01

Input Form

HypergeometricPFQ[{-(11/2)}, {7/2, 9/2}, -z] == (1/(19025362944 z^(7/2))) (2 Sqrt[z] (196465500 - 874458585 z + 1482846750 z^2 + 2042364618 z^3 + 357520356 z^4 + 19364310 z^5 + 397596 z^6 + 3164 z^7 + 8 z^8) Cos[2 Sqrt[z]] + (-196465500 - 278139015 z + 564510870 z^2 + 1769748750 z^3 + 340152372 z^4 + 18983610 z^5 + 394476 z^6 + 3156 z^7 + 8 z^8) Sin[2 Sqrt[z]] + 16 z (88409475 - 235758600 z + 550103400 z^2 + 550103400 z^3 + 91683900 z^4 + 4889808 z^5 + 99792 z^6 + 792 z^7 + 2 z^8) 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]