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In mathematics, the Jacobi–Anger expansion (or Jacobi–Anger identity) is an expansion of exponentials of trigonometric functions in the basis of their harmonics. It is uful in physics (for example, to convert between plane waves and cylindrical waves), and in signal processing (to describe FM signals). This identity is named after the 19th-century mathematicians Carl Jacobi and Carl Theodor Anger.
考研政治冲刺The most general identity is given by:[1][2]吸血鬼日记片尾曲
where J n(z) is the n-th Besl function. Using the relation valid for integer n, the expansion becomes:[1][2]
The following real-valued variations are often uful as well:[3]
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1.
^ a b Colton & Kress (1998) p. 32.
2.
the rasmus^ a b Cuyt et al. (2008) p. 344.成都o培训
英语手抄报简单3.
^ Abramowitz & Stegun (1965) p. 361, 9.1.42–45 (www.math.sfu.ca/~cbm/aands/page_361.ht
m)
四六级成绩查询时间Abramowitz, Milton; Stegun, Irene A., eds. (1965), "Chapter 9" (www.math.sfu.ca
/~cbm/aands/page_355.htm) , Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, pp. 355, MR0167642 (www.ams
/mathscinet-getitem?mr=0167642) , ISBN 978-0486612720, www.math.sfu.ca
/~cbm/aands/page_355.htm.
Colton, David; Kress, Rainer (1998), Inver acoustic and electromagnetic scattering theory, Applied Mathematical Sciences, 93 (2nd ed.), ISBN 978-3-540-62838-5
Cuyt, Annie; Petern, Vigdis; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B.
(2008), Handbook of continued fractions for special functions, Springer,
ISBN 978-1-4020-6948-2
Weisstein, Eric W.. "Jacobi–Anger expansion" (/Jacobi-
AngerExpansion.html) . MathWorld — a Wolfram web resource.
/Jacobi-AngerExpansion.html. Retrieved 2008-11-11. Retrieved from "en.wikipedia/wiki/Jacobi%E2%80%93Anger_expansion"
Categories: Special functions | Mathematical identities
gto什么意思This page was last modified on 4 May 2010 at 04:58.
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