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

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.aaks.01

Input Form

HypergeometricPFQ[{-(3/4)}, {-(11/2), -(21/4)}, z] == (1/(723647925 Sqrt[2])) (z^(1/4) ((723647925 + 1428499800 z + 830662560 z^2 + 127284480 z^3 + 8644608 z^4 + 278528 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (723647925 + 849581460 z + 202456800 z^2 + 19400256 z^3 + 897024 z^4 + 16384 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 36 z (80405325 + 30073680 z + 4153968 z^2 + 267264 z^3 + 8192 z^4) 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]