Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9oa)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9oa.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 9/4}, z] == (1/(29072736 Sqrt[2] z^(13/4))) ((-4 z (893025 - 567000 z - 19015416 z^2 + 16781184 z^3 - 1763328 z^4 + 32768 z^5) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (1488375 - 812700 z - 3360420 z^2 + 7643328 z^3 - 867328 z^4 + 16384 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-22325625 + 10206000 z - 11340000 z^2 - 32266080 z^3 + 61963776 z^4 - 6955008 z^5 + 131072 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]