Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1340)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=6

http://functions.wolfram.com/07.22.03.1340.01

Input Form

HypergeometricPFQ[{-(7/2)}, {6, 6}, -z] == (1/(5277564317025 z^(9/2))) (512 (Sqrt[z] (173675502000 - 257130290025 z + 124483489200 z^2 - 40168850400 z^3 + 25481131200 z^4 + 6261776640 z^5 + 292859904 z^6 + 4149248 z^7 + 16384 z^8) BesselJ[0, Sqrt[z]]^2 - 16 (21709437750 - 23577376725 z + 10097206875 z^2 - 3199788900 z^3 + 1327441500 z^4 + 378060480 z^5 + 18110976 z^6 + 258560 z^7 + 1024 z^8) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + Sqrt[z] (360882855900 - 344880599175 z + 150984842400 z^2 - 49006490400 z^3 + 22557528000 z^4 + 6118407936 z^5 + 290797568 z^6 + 4141056 z^7 + 16384 z^8) 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]