Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7z5)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a7z5.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(9/2), 15/4}, -z] == ((2 Sqrt[z] (-1224171073125 + 771891120000 z + 430026105600 z^2 - 144025190400 z^3 + 14768209920 z^4 - 713031680 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (3672513219375 - 7911883980000 z - 555761606400 z^2 + 154648166400 z^3 - 15242035200 z^4 + 723517440 z^5 - 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (3672513219375 - 77189112000 z + 473426553600 z^2 - 148026654720 z^3 + 14953021440 z^4 - 717225984 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(772905369600 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]