Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0784)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=-5/2

http://functions.wolfram.com/07.22.03.0784.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(5/2), 5}, -z] == (1/(172297125 z^(7/2))) (8 (-2 BesselJ[1, 2 Sqrt[z]] (-383107725 + 216112050 z + 14288400 z^2 - 1587600 z^3 + 187200 z^4 - 36864 z^5 + 18432 z^6 - 77824 z^7 - 2048 z^8 + 512 Pi z^(15/2) (153 + 4 z) StruveH[0, 2 Sqrt[z]]) + Sqrt[z] BesselJ[0, 2 Sqrt[z]] (-766215450 + 49116375 z - 10716300 z^2 + 1134000 z^3 - 169920 z^4 + 52992 z^5 - 76800 z^6 - 315392 z^7 - 8192 z^8 + 1024 Pi z^7 (153 + 4 z) StruveH[1, 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]