Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0602)

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

For fixed z and a₁=-11/2, b₁=3

http://functions.wolfram.com/07.22.03.0602.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3, 3}, -z] == (1/(4108830350625 z^(3/2))) (8 (Sqrt[z] (-21070924875 + 652968993600 z + 866349237600 z^2 + 221439614400 z^3 + 17184326400 z^4 + 483747840 z^5 + 5074944 z^6 + 16384 z^7) BesselJ[0, Sqrt[z]]^2 - 2 (-21070924875 + 125966194200 z + 362484460800 z^2 + 104659192800 z^3 + 8414956800 z^4 + 239984640 z^5 + 2531328 z^6 + 8192 z^7) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + Sqrt[z] (-64131484725 + 344484478800 z + 767160655200 z^2 + 213195038400 z^3 + 16946208000 z^4 + 481222656 z^5 + 5066752 z^6 + 16384 z^7) 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]