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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(7/2), -(11/4)}, z] == -((1/(1596827925 z^(1/4))) (Sqrt[2] ((-1596827925 + 2239706700 z + 107442720 z^2 - 1360941120 z^3 + 32089559040 z^4 + 48399777792 z^5 + 2240806912 z^6 + 4194304 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-1596827925 + 110602800 z + 660456720 z^2 - 606735360 z^3 + 20715909120 z^4 + 6687424512 z^5 + 77594624 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-1596827925 - 2018501100 z - 1625334480 z^2 - 2359526400 z^3 + 7454638080 z^4 + 502792192 z^5 + 1048576 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]