2003/10/18 by Vivek V Rane
Mathematics · #math.NT
published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 213-221 · 9 pages
arxiv created 2003/10/18 · arxiv updated 2009/12/01
Euler--Maclaurin and Poisson analogues of the summations ∑a < n ≤ b χ(n) f(n), ∑a < n ≤ b d(n) f(n), ∑a < n ≤ b d(n) χ(n) f(n) have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence; d(n) is the divisor function and f(x) is a sufficiently smooth function on [a,b]. We also state a generalised Abel's summation formula, generalised Euler's summation formula and Euler's summation formula in several variables.