Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0380)

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/07.22.03.0380.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(9/2), 5}, -z] == (1/(206239658625 z^(7/2))) (8 (-2 BesselJ[1, 2 Sqrt[z]] (-1074617168625 + 674269596000 z + 18261468225 z^2 - 432224100 z^3 + 14288400 z^4 - 705600 z^5 + 57600 z^6 - 9216 z^7 + 4096 z^8 - 16384 z^9 + 16384 Pi z^(19/2) StruveH[0, 2 Sqrt[z]]) + Sqrt[z] BesselJ[0, 2 Sqrt[z]] (-2149234337250 + 273922023375 z - 5618913300 z^2 + 157172400 z^3 - 6350400 z^4 + 403200 z^5 - 46080 z^6 + 12288 z^7 - 16384 z^8 - 65536 z^9 + 32768 Pi z^9 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]