Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a94g)

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

For fixed z and a₁=-11/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a94g.01

Input Form

HypergeometricPFQ[{-(11/4)}, {5/2, 15/4}, z] == -(((2 Sqrt[z] (16081065 - 183783600 z - 1820588544 z^2 + 872882176 z^3 - 67567616 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^2 + (-48243195 + 477837360 z + 1376331264 z^2 - 832413696 z^3 + 66912256 z^4 - 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (48243195 + 402793776 z + 1626831360 z^2 - 856399872 z^3 + 67305472 z^4 - 1048576 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(2444083200 Sqrt[2] z^(9/4)))

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]