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

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-3/2

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

Input Form

HypergeometricPFQ[{9/4}, {-(3/2), 23/4}, z] == (1/(8388608 Sqrt[2] z^(17/4))) (4389 (-26 Sqrt[z] (30925125 + 32044320 z + 4112640 z^2 + 131072 z^3) BesselI[-(1/4), Sqrt[z]]^2 + (1206079875 + 3087564480 z + 766321920 z^2 + 48562176 z^3 + 524288 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 18 Sqrt[z] (134008875 + 57177120 z + 6732544 z^2 + 196608 z^3) 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]