Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa5u)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.aa5u.01

Input Form

HypergeometricPFQ[{-(5/4)}, {-(11/2), 17/4}, z] == -((13 (2 Sqrt[z] (44358635475 - 49569014880 z - 2070706176 z^2 + 404447232 z^3 + 14483456 z^4) BesselI[1/4, Sqrt[z]]^2 - 3 (73931059125 - 135188222400 z - 22482915840 z^2 + 8830976 z^3 + 14483456 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (221793177375 + 67594111200 z + 4651637760 z^2 + 442834944 z^3 + 14483456 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (10173284352 Sqrt[2] z^(11/4)))

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]