Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag27)

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`=-3/2

http://functions.wolfram.com/07.22.03.ag27.01

Input Form

HypergeometricPFQ[{21/4}, {-(3/2), -(17/4)}, -z] == -((1/(296709075 Sqrt[2])) (z^(1/4) ((-296709075 + 837766800 z - 1314649440 z^2 + 285143040 z^3 + 1916780544 z^4 - 580386816 z^5 + 2097152 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 + 4 Sqrt[z] (-296709075 + 600399540 z - 855429120 z^2 - 1580156928 z^3 - 1018036224 z^4 + 29622272 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (296709075 - 363032280 z - 329688576 z^2 + 256536576 z^3 - 137822208 z^4 + 524288 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]