Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a85t)

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`=1/2

http://functions.wolfram.com/07.22.03.a85t.01

Input Form

HypergeometricPFQ[{-(15/4)}, {1/2, 15/4}, -z] == ((2 Sqrt[z] (-638512875 - 324324000 z + 20381587200 z^2 + 77491814400 z^3 + 22819307520 z^4 + 1331691520 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - (-1915538625 + 1945944000 z - 2594592000 z^2 + 65271398400 z^3 + 22015180800 z^4 + 1321205760 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1915538625 + 2140538400 z + 7783776000 z^2 + 72276295680 z^3 + 22492938240 z^4 + 1327497216 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(44856115200 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]