Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9357)

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`=-1/2

http://functions.wolfram.com/07.22.03.9357.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), -(5/4)}, -z] == -((1/(43875 Sqrt[2])) (z^(1/4) ((-43875 - 245700 z + 5616000 z^2 + 8193920 z^3 + 1269760 z^4 + 32768 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (43875 + 280800 z + 931920 z^2 + 156160 z^3 + 4096 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 4 z (-43875 + 1000800 z + 1972320 z^2 + 315392 z^3 + 8192 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]