Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0454)

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=-3/2

http://functions.wolfram.com/07.22.03.0454.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(3/2), 1}, -z] == (1/93555) (2 Sqrt[z] BesselJ[1, 2 Sqrt[z]] (-4 (12744 - 17892 z + 113472 z^2 + 29049 z^3 + 1448 z^4 + 16 z^5) + Pi z^(5/2) (480249 + 117612 z + 5808 z^2 + 64 z^3) StruveH[0, 2 Sqrt[z]]) + BesselJ[0, 2 Sqrt[z]] (93555 - 147528 z + 406800 z^2 + 2034432 z^3 + 476208 z^4 + 23296 z^5 + 256 z^6 - 2 Pi z^3 (480249 + 117612 z + 5808 z^2 + 64 z^3) 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]