Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2000)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-3/2, b_1`>=-11/2

For fixed z and a₁=-3/2, b₁=4

http://functions.wolfram.com/07.22.03.2000.01

Input Form

HypergeometricPFQ[{-(3/2)}, {4, 5}, -z] == (1/(1091475 z^3)) (64 (z (53865 - 43488 z + 40896 z^2 + 9600 z^3 + 256 z^4) BesselJ[0, Sqrt[z]]^2 - 8 Sqrt[z] (11340 - 7569 z + 4266 z^2 + 1176 z^3 + 32 z^4) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + (-34020 + 84033 z - 57528 z^2 + 36288 z^3 + 9472 z^4 + 256 z^5) BesselJ[1, Sqrt[z]]^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]