Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a89k)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a89k.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, 7/4}, z] == (1/(1754298000 Sqrt[2] z^(7/4))) ((2 z (6548850 + 1129799475 z - 1108360800 z^2 + 175703040 z^3 - 6922240 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]]^2 - Sqrt[z] (39293100 + 661901625 z - 1009411200 z^2 + 171486720 z^3 - 6881280 z^4 + 65536 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (29469825 - 144074700 z - 1819644750 z^2 + 2134036800 z^3 - 347996160 z^4 + 13811712 z^5 - 131072 z^6) 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]