Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9m2)

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`=9/2

http://functions.wolfram.com/07.22.03.a9m2.01

Input Form

HypergeometricPFQ[{-(9/4)}, {9/2, -(23/4)}, z] == (1/(1663721928 Sqrt[2] z^(9/4))) ((-4 z (-47539238175 + 424431216 z + 956362752 z^2 + 60358656 z^3 + 1048576 z^4) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-79232063625 - 4949029800 z + 477674112 z^2 + 30638080 z^3 + 524288 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (1188480954375 + 179878198500 z + 12459096000 z^2 + 4010655744 z^3 + 244580352 z^4 + 4194304 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]