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

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`=-11/2

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

Input Form

HypergeometricPFQ[{7/4}, {-(11/2), 17/4}, z] == (1/(181665792 Sqrt[2] z^(11/4))) (13 (-2 Sqrt[z] (-133075906425 + 128428811280 z + 27108652032 z^2 + 1540718592 z^3 + 21757952 z^4) BesselI[1/4, Sqrt[z]]^2 + (-665379532125 + 1115302834800 z + 390737571840 z^2 + 35352920064 z^3 + 973602816 z^4 + 4194304 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (665379532125 + 304173500400 z + 41864739840 z^2 + 1923514368 z^3 + 23330816 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]