Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad4o)

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.ad4o.01

Input Form

HypergeometricPFQ[{7/4}, {7/2, -(23/4)}, z] == (1/(605682 Sqrt[2] z^(5/4))) ((8 z (100083753 + 15834672 z + 661248 z^2 + 4096 z^3) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (333107775 + 83041392 z + 5854464 z^2 + 102400 z^3) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (4996616625 + 1695821400 z + 184173696 z^2 + 6236160 z^3 + 32768 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]