Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8935)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8935.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 5/4}, -z] == ((2 (566645795100 + 1745113055301 z + 1196563260816 z^2 + 209696610816 z^3 + 11371143168 z^4 + 205062144 z^5 + 1048576 z^6) BesselJ[1/4, Sqrt[z]]^2 - 3 Sqrt[z] (946465342515 + 1028600684496 z + 200042777088 z^2 + 11193262080 z^3 + 204144640 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 (8683775100 + 1024369152345 z + 1049891374224 z^2 + 201366950400 z^3 + 11218378752 z^4 + 204275712 z^5 + 1048576 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(566645795100 Sqrt[2] z^(1/4))

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]