Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agm0)

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.agm0.01

Input Form

HypergeometricPFQ[{23/4}, {3/2, -(23/4)}, z] == (1/(99687686175 z^(1/4))) (Sqrt[2] ((99687686175 - 265833829800 z + 185032149120 z^2 - 5708795904 z^3 - 6539968512 z^4 + 737673216 z^5 + 8388608 z^6) BesselI[1/4, Sqrt[z]]^2 + 28 Sqrt[z] (14241098025 - 13053949200 z - 5877020160 z^2 + 2035703808 z^3 - 151191552 z^4 + 11534336 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 8 z (23881799025 + 33231416400 z - 6273953280 z^2 - 376922112 z^3 + 62717952 z^4 + 1048576 z^5) 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]