Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae8m)

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`=-7/2

http://functions.wolfram.com/07.22.03.ae8m.01

Input Form

HypergeometricPFQ[{13/4}, {-(7/2), 23/4}, z] == (1/(251658240 Sqrt[2] z^(17/4))) (209 (2 Sqrt[z] (1923697400625 + 2105241138000 z + 374250240000 z^2 + 25472778240 z^3 + 702545920 z^4 + 4194304 z^5) BesselI[-(1/4), Sqrt[z]]^2 - (5771092201875 + 15109768674000 z + 4533774336000 z^2 + 464212869120 z^3 + 19920322560 z^4 + 297795584 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (5771092201875 + 2798105310000 z + 440545996800 z^2 + 28163358720 z^3 + 740818944 z^4 + 4194304 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]