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

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`=-11/2

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

Input Form

HypergeometricPFQ[{3/4}, {-(11/2), 21/4}, z] == (221 (-6 Sqrt[z] (-642566519595 + 642144056400 z + 108150577920 z^2 + 4511952896 z^3 + 38797312 z^4) BesselI[1/4, Sqrt[z]]^2 + (-9638497793925 + 16486203721680 z + 5083077162240 z^2 + 358840627200 z^3 + 6628048896 z^4 + 16777216 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 18 Sqrt[z] (1070944199325 + 452880545040 z + 53216951040 z^2 + 1745203200 z^3 + 13631488 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(3875536896 Sqrt[2] z^(15/4))

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]