On an identity by Chaundy and Bullard. II. More history
نویسندگان
چکیده
An identity by Chaundy and Bullard writes 1/(1− x)n (n = 1,2, . . .) as a sum of two truncated binomial series. In a paper which appeared in 2008 in Indag. Math. the authors surveyed many aspects of this identity. In the present paper we discuss much earlier occurrences of this identity in works by Hering (1868), de Moivre (1738) and de Montmort (1713). A relationship with Krawtchouk polynomials in work by Greville (1966) is also discussed.
منابع مشابه
On an identity by Chaundy and Bullard. I
An identity by Chaundy and Bullard writes 1/(1 − x)n (n = 1, 2, . . .) as a sum of two truncated binomial series. A special case of this identity was rediscovered by I. Daubechies, while she was setting up the theory of wavelets of compact support. We present at least six different proofs of this identity. The paper concludes with a multivariable analogue of the identity.
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تاریخ انتشار 2012