Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8xw)

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.a8xw.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(5/2), 19/4}, z] == ((2 Sqrt[z] (92868150375 + 71013983040 z - 6469182720 z^2 + 5504139264 z^3 + 1855782912 z^4 + 222298112 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (278604451125 + 637582065120 z + 5292967680 z^2 + 7232569344 z^3 + 2022899712 z^4 + 232783872 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-278604451125 - 43225902720 z - 3646266624 z^2 + 6085804032 z^3 + 1917911040 z^4 + 226492416 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(9814671360 Sqrt[2] z^(13/4))

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]