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

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{7/4}, {-(11/2), -(23/4)}, z] == (1/(47220482925 z^(1/4))) (Sqrt[2] (3 (15740160975 - 30609324900 z + 8807475600 z^2 + 5470819200 z^3 + 985501440 z^4 + 104853504 z^5 + 9764864 z^6 + 9437184 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (47220482925 - 28867330800 z - 24059851200 z^2 - 5428684800 z^3 - 668505600 z^4 - 60530688 z^5 - 2752512 z^6 + 2097152 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (15740160975 + 11364437700 z + 3135132000 z^2 + 453499200 z^3 + 45327360 z^4 + 4440064 z^5 + 1835008 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]