Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8938)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8938.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 9/4}, z] == ((2 Sqrt[z] (48852594525735 - 103712307963264 z + 48262896734976 z^2 - 6183017938944 z^3 + 262238699520 z^4 - 3875536896 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 - 3 (2846107289025 - 69147913554720 z + 43215780351744 z^2 - 5959171620864 z^3 + 258872377344 z^4 - 3860856832 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (4925871425475 - 72897942237120 z + 43872495803136 z^2 - 5990103318528 z^3 + 259348561920 z^4 - 3862953984 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (47144930152320 Sqrt[2] z^(3/4))

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]