Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0814)

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=-3/2

http://functions.wolfram.com/07.22.03.0814.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(3/2), 11/2}, -z] == (1/(294912 z^(9/2))) (2 Sqrt[z] (-4465125 + 1063125 z + 68040 z^2 - 28350 z^3 + 7578 z^4 - 3654 z^5 + 8760 z^6 + 644 z^7 + 8 z^8) Cos[2 Sqrt[z]] + (4465125 - 7016625 z - 238140 z^2 - 107730 z^3 + 28350 z^4 - 9378 z^5 + 8160 z^6 + 636 z^7 + 8 z^8) Sin[2 Sqrt[z]] + 32 z^7 (1134 + 81 z + z^2) 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]