Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0984)

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=9/2

http://functions.wolfram.com/07.22.03.0984.01

Input Form

HypergeometricPFQ[{-(9/2)}, {9/2, 11/2}, -z] == (1/(1207959552 z^(9/2))) (2 Sqrt[z] (-125023500 + 292699575 z - 218289330 z^2 + 160886250 z^3 + 95926644 z^4 + 8767350 z^5 + 252732 z^6 + 2588 z^7 + 8 z^8) Cos[2 Sqrt[z]] + (125023500 + 183580425 z - 178894170 z^2 + 100047150 z^3 + 88395300 z^4 + 8528346 z^5 + 250188 z^6 + 2580 z^7 + 8 z^8) Sin[2 Sqrt[z]] + 16 z (-40186125 + 64297800 z - 50009400 z^2 + 50009400 z^3 + 25004700 z^4 + 2222640 z^5 + 63504 z^6 + 648 z^7 + 2 z^8) 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]