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

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=7/2

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

Input Form

HypergeometricPFQ[{-(3/4)}, {7/2, 19/4}, z] == -((1/(7667712 Sqrt[2] z^(13/4))) (11 (2 Sqrt[z] (135135 - 730080 z - 608256 z^2 - 729088 z^3 + 65536 z^4) BesselI[-(1/4), Sqrt[z]]^2 + (-405405 + 1572480 z + 953856 z^2 + 688128 z^3 - 65536 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (405405 + 1046304 z + 764928 z^2 + 712704 z^3 - 65536 z^4) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]