Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9564)

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`=7/2

http://functions.wolfram.com/07.22.03.9564.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 11/4}, z] == -(((2 z (-2943161246025 - 46063262044800 z + 34888112812800 z^2 - 5279034408960 z^3 + 242635571200 z^4 - 3758096384 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 + Sqrt[z] (7690717309275 + 30831731330400 z - 31955168044800 z^2 + 5133504430080 z^3 - 240314941440 z^4 + 3747610624 z^5 - 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 (854074821600 + 7113246265125 z + 39021236654400 z^2 - 33656528505600 z^3 + 5219812638720 z^4 - 241702600704 z^5 + 3753902080 z^6 - 16777216 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (66514960512000 Sqrt[2] z^(7/4)))

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]