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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{19/4}, {11/2, -(23/4)}, z] == (1/(177666720 Sqrt[2] z^(13/4))) ((-4 z (31835443164525 + 7296392703600 z + 720335024640 z^2 + 42090209280 z^3 + 1685913600 z^4 + 32505856 z^5) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (159177215822625 + 50631049368900 z + 6361231060800 z^2 + 444466391040 z^3 + 20626636800 z^4 + 596901888 z^5 + 4194304 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - (795886079113125 + 323900676099000 z + 51890196758400 z^2 + 4404911616000 z^3 + 237011927040 z^4 + 8642887680 z^5 + 142606336 z^6) 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]