spherical harmonics

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spherical harmonics

[′sfir·ə·kəl här′män·iks]
(mathematics)
Solutions of Laplace's equation in spherical coordinates.
References in periodicals archive ?
Pariiskii, Evaluation of prolate spheroidal function by solving the corresponding differential equations, U.S.S.R.
The author of [26] called these solutions generalized prolate spheroidal functions, and investigated various asymptotic cases, e.g.
Slavyanov, Spheroidal and Coulomb Spheroidal Functions, [in Russian], Nauka, Moscow, 1976.
Classical mathematical physics books, such as Morse and Feshbach [4], Whittaker and Watson [18], or the Batemann Manuscript [19], have sections or chapters on the special forms of the Heun equation like Mathieu, Lame, or spheroidal functions. Some papers on different mathematical properties of these functions can be found in [8, 20-25].
Separation of variables is possible only if l = 0 [15], and it leads to a representation of the field that utilizes spheroidal functions.
Slavyanov, Spheroidal and Coulomb Spheroidal Functions, Nauka, Moscow, 1976 (in Russian).
Spheroidal functions are not easy to compute especially in the case of high frequencies when they contain the large parameter kp, where p is the focal distance.
Slavyanov, Spheroidal and Coulomb Spheroidal Functions, Science, Moscow, 1976 (in Russian).
Approximation of an analytic function on a finite real interval by a bandlimited function and conjectures on properties of prolate spheroidal functions. Appl.