• Analogues of Euler and Poisson summation formulae

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/113/03/0213-0221

• # Keywords

Abel’s summation formula; Euler summation formula; Euler-Maclaurin summation formula; Poisson’s summation formula; Fourier series

• # Abstract

Euler-Maclaurin and Poisson analogues of the summations εa &lt;nb 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 andf(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.

• # Author Affiliations

1. Department of Mathematics, The Institute of Science, 15, Madam Cama Road, Mumbai - 400 032, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019