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

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), 19/4}, z] == ((2 Sqrt[z] (14235360764625 + 17108415324000 z + 4581624902400 z^2 + 666365706240 z^3 + 79330344960 z^4 + 3063939072 z^5 - 218103808 z^6) BesselI[-(1/4), Sqrt[z]]^2 + (-42706082293875 - 116401180896000 z - 45979047878400 z^2 - 8189308108800 z^3 - 1040619601920 z^4 - 87048585216 z^5 + 1291845632 z^6 + 134217728 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (42706082293875 + 25294872002400 z + 5899520390400 z^2 + 823405363200 z^3 + 90763100160 z^4 + 2837446656 z^5 - 234881024 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(15642132480 Sqrt[2] z^(13/4))

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]