Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae76)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ae76.01

Input Form

HypergeometricPFQ[{13/4}, {-(9/2), 19/4}, z] == -((1/(141557760 Sqrt[2] z^(13/4))) (11 (2 Sqrt[z] (384739480125 + 431223156000 z + 86077555200 z^2 + 7145594880 z^3 + 262799360 z^4 + 2097152 z^5) BesselI[-(1/4), Sqrt[z]]^ 2 - (1154218440375 + 3052478520000 z + 986951347200 z^2 + 117478932480 z^3 + 6444810240 z^4 + 130023424 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (1154218440375 + 590145847200 z + 103186137600 z^2 + 8027873280 z^3 + 279576576 z^4 + 2097152 z^5) 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]