Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8344)

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`=5/2

http://functions.wolfram.com/07.22.03.8344.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(9/4)}, z] == -(((16 z (-10703093625 - 17911706400 z - 10805414400 z^2 - 8343552000 z^3 + 2450083840 z^4 - 109445120 z^5 + 1048576 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 + 4 Sqrt[z] (26233601625 + 47326960800 z + 26028576000 z^2 + 13967769600 z^3 - 4766883840 z^4 + 217579520 z^5 - 2097152 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (-78700804875 + 251842575600 z + 336908678400 z^2 + 193858560000 z^3 + 124349644800 z^4 - 38770114560 z^5 + 1746927616 z^6 - 16777216 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(136271362500 Sqrt[2] z^(3/4)))

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]