Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0878)

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=1

http://functions.wolfram.com/07.22.03.0878.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1, 7/2}, -z] == (1/(1300561920 z^2)) (4 (2 z (2679075 + 170190720 z + 552042288 z^2 + 227492352 z^3 + 21481728 z^4 + 581632 z^5 + 4096 z^6) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (8037225 + 21432600 z + 454665456 z^2 + 217241856 z^3 + 21194496 z^4 + 579584 z^5 + 4096 z^6) BesselJ[1, 2 Sqrt[z]]) + Pi (8037225 + 25004700 z + 300056400 z^2 + 2000376000 z^3 + 889056000 z^4 + 85349376 z^5 + 2322432 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (8037225 + 25004700 z + 300056400 z^2 + 2000376000 z^3 + 889056000 z^4 + 85349376 z^5 + 2322432 z^6 + 16384 z^7) BesselJ[0, 2 Sqrt[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]