Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0944)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=3

http://functions.wolfram.com/07.22.03.0944.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3, 3}, -z] == (1/(18261468225 z^(3/2))) (8 (Sqrt[z] (-127702575 + 3003875280 z + 3443277600 z^2 + 710866944 z^3 + 41515776 z^4 + 780288 z^5 + 4096 z^6) BesselJ[0, Sqrt[z]]^2 - 2 (-127702575 + 644242410 z + 1486401840 z^2 + 340502688 z^3 + 20468736 z^4 + 388608 z^5 + 2048 z^6) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + Sqrt[z] (-371648655 + 1707622560 z + 3116686176 z^2 + 690681600 z^3 + 41128704 z^4 + 778240 z^5 + 4096 z^6) 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]