Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9128)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9128.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 7/4}, z] == ((2 Sqrt[z] (60162465825 + 67162510800 z + 13198671360 z^2 + 1104650240 z^3 + 47775744 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^ 2 - (-114577588125 + 77986616400 z + 13981524480 z^2 + 1136271360 z^3 + 48431104 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (114577588125 + 71001176400 z + 13495426560 z^2 + 1117003776 z^3 + 48037888 z^4 + 1048576 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(196709990400 Sqrt[2] z^(1/4))

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]