Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0371)

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=-9/2

http://functions.wolfram.com/07.22.03.0371.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(9/2), 3}, z] == (1/(1915538625 z^(3/2))) (2 (BesselI[1, 2 Sqrt[z]] (-1404728325 + 216112050 z + 7144200 z^2 + 352800 z^3 + 28800 z^4 + 4608 z^5 + 2048 z^6 + 8192 z^7 + 8192 Pi z^(15/2) StruveL[0, 2 Sqrt[z]]) - Sqrt[z] BesselI[0, 2 Sqrt[z]] (-1404728325 - 39293100 z - 1587600 z^2 - 100800 z^3 - 11520 z^4 - 3072 z^5 - 4096 z^6 + 16384 z^7 + 8192 Pi z^7 StruveL[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]