Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9gm)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a9gm.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(1/2), 21/4}, z] == (17 (2 Sqrt[z] (1039863825 - 1362160800 z + 247484160 z^2 + 69746688 z^3 - 43057152 z^4 - 195035136 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (-1733106375 + 3502699200 z - 172972800 z^2 + 145981440 z^3 + 188940288 z^4 + 180355072 z^5 - 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (5199319125 + 583783200 z + 74131200 z^2 - 103956480 z^3 - 172818432 z^4 - 182452224 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (2906652672 Sqrt[2] z^(15/4))

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]