Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afj8)

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`=-9/2

http://functions.wolfram.com/07.22.03.afj8.01

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), 21/4}, z] == -((221 (2 Sqrt[z] (-5189960350575 + 4522046039280 z + 1496664449280 z^2 + 186931261440 z^3 + 13997506560 z^4 + 846200832 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 - (-25949801752875 + 41063422554000 z + 19163584661760 z^2 + 3057676554240 z^3 + 267216814080 z^4 + 17222860800 z^5 + 687865856 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (25949801752875 + 14296154518800 z + 2899133233920 z^2 + 304551383040 z^3 + 21332951040 z^4 + 1116733440 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (38149816320 Sqrt[2] z^(15/4)))

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]