Abstract
1. It is known that any polynomial in μ. can be expanded as a linear function of Legendre polynomials [1]. In particular, we haveThe earlier coefficients, say A0, A2, A4 may easily be found by equating the coefficients of μp+q, μp+q-2, μp+q-4 on the two sides of (1). The general coefficient A2k might then be surmised, and the value verified by induction. This may have been the method followed by Ferrers, who stated the result as an exercise in his Spherical Harmonics (1877). A proof was published by J. C. Adams [2]. The proof now to be given follows different lines from his.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference9 articles.
1. A Chapter from Ramanujan's Notebook;Hardy;Proc. Camb. Phil. Soc.,1923
2. III. On the expression of the product of any two legendre’s coefficients by means of a series of Legendre’s coefficients
3. On Vandermonde's Theorem, and some general Expansions;Dougall;Proc Edin. Math. Soc.,1907
4. 1. MacRobert T. M. , Spherical Harmonics (London), p. 95.
Cited by
18 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献