Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9221)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.9221.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 3/4}, -z] == (1/(12700800 Sqrt[2])) (z^(1/4) (2 (6350400 - 11354175 z + 6635520 z^2 - 1681920 z^3 + 360448 z^4 + 65536 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + Sqrt[z] (12289725 - 7529760 z + 1797120 z^2 - 319488 z^3 - 65536 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 z (-13111875 + 7076160 z - 1746432 z^2 + 344064 z^3 + 65536 z^4) 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]