Combinatorial formulae for the derivatives of Lamé functions
نویسنده
چکیده
Lamé functions play a central role in the theory of ellipsoidal harmonics and have many varied applications in mathematical physics. In this article, a generalized approach to the computation of Lamé function derivatives of arbitrary order is derived and it is demonstrated how these derivatives can be expressed recursively in terms of the original Lamé functions by making use of combinatorial formulae discovered by di Bruno, Girard and Waring. 2006 Elsevier Inc. All rights reserved.
منابع مشابه
Certain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces
We study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...
متن کاملOn Eigenvalues of Lamé Operator
We introduce two integral representations of monodromy on Lamé equation. By applying them, we obtain results on hyperelliptic-to-elliptic reduction integral formulae, finite-gap potential and eigenvalues of Lamé operator.
متن کاملInvariant Cubature Formulae for Spheres and Balls by Combinatorial Methods
Invariant cubature formulae for a class of weight functions on the simplex T d are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282–290] for the unit weight function on T . These formulae are used to derive cubature formulae on the surface of the sphere S and on the unit ball B using connections between cubature formul...
متن کاملOstrowski type inequalities for functions whose derivatives are preinvex
In this paper, making use of a new identity, we establish new inequalities of Ostrowski type for the class of preinvex functions and gave some midpoint type inequalities.
متن کاملSchur Q-functions and spin characters of symmetric groups I
In a classic paper, I. Schur [6] introduced a class of symmetric functions, now called Schur Qfunctions, in order to determine the irreducible spin (projective) characters of symmetric groups. In the case of the ordinary characters of symmetric groups, going back to the early work of D. E. Littlewood and A. R. Richardson [3], the corresponding Schur functions have been used to give useful combi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Applied Mathematics and Computation
دوره 182 شماره
صفحات -
تاریخ انتشار 2006