Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1526)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=-1/2

http://functions.wolfram.com/07.22.03.1526.01

Input Form

HypergeometricPFQ[{-(5/2)}, {-(1/2), 6}, -z] == (1/(135135 z^(9/2))) (8 ((-BesselJ[1, 2 Sqrt[z]]) (-3742200 + 2466450 z + 33075 z^2 + 11700 z^3 - 3600 z^4 + 2112 z^5 - 9472 z^6 - 512 z^7 + 128 Pi z^(13/2) (75 + 4 z) StruveH[0, 2 Sqrt[z]]) + 2 Sqrt[z] BesselJ[0, 2 Sqrt[z]] (-1871100 + 297675 z + 9450 z^2 - 3600 z^3 + 1440 z^4 - 2304 z^5 - 9728 z^6 - 512 z^7 + 64 Pi z^6 (75 + 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]