Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7xt)

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`=-11/2

http://functions.wolfram.com/07.22.03.a7xt.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(11/2), 15/4}, -z] == ((2 Sqrt[z] (-5771092201875 + 3997293300000 z + 1430905132800 z^2 - 392443084800 z^3 + 31713853440 z^4 - 1121976320 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (17313276605625 - 38374015680000 z - 1014485472000 z^2 + 414343987200 z^3 - 32443269120 z^4 + 1132462080 z^5 - 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (17313276605625 - 1439025588000 z + 1543782240000 z^2 - 400840704000 z^3 + 32000901120 z^4 - 1126170624 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2429131161600 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]