Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.5989)

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=6, b_1`>=-11/2

For fixed z and a₁=6, b₁=-5/2

http://functions.wolfram.com/07.22.03.5989.01

Input Form

HypergeometricPFQ[{6}, {-(5/2), 7/2}, -z] == (1/(57600 z)) (-15 Pi Sqrt[z] (-900 + 645 z - 600 z^2 + 464 z^3) StruveH[2, 2 Sqrt[z]] + 2 (8 z (3600 + 2340 z + 1365 z^2 + 1160 z^3 - 16 z^4) + 15 Pi (-1350 + 1080 z - 975 z^2 - 600 z^3 + 16 z^4) StruveH[3, 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]