Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8308)

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`=3/2

http://functions.wolfram.com/07.22.03.8308.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 3/4}, z] == (1/(434188755000 Sqrt[2])) (z^(1/4) ((434188755000 - 3163630828050 z + 2479017895200 z^2 - 436011033600 z^3 + 23322542080 z^4 - 414842880 z^5 + 2097152 z^6) BesselI[-(1/4), Sqrt[z]]^2 + Sqrt[z] (1066424557275 - 1120593474000 z + 211053427200 z^2 - 11533393920 z^3 + 206766080 z^4 - 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 (62960643900 - 1339151415525 z + 1189200474000 z^2 - 215169292800 z^3 + 11609825280 z^4 - 207159296 z^5 + 1048576 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]