Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0856)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=1/2

http://functions.wolfram.com/07.22.03.0856.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1/2, 7/2}, -z] == (1/(516096 z^(5/2))) (2 Sqrt[z] (-8505 - 14175 z + 151074 z^2 + 125073 z^3 + 15630 z^4 + 502 z^5 + 4 z^6) Cos[2 Sqrt[z]] + (8505 + 2835 z + 85050 z^2 + 111951 z^3 + 15150 z^4 + 498 z^5 + 4 z^6) Sin[2 Sqrt[z]] + 8 z^3 (99225 + 66150 z + 7938 z^2 + 252 z^3 + 2 z^4) SinIntegral[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]