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

Euler-Maclaurin and Poisson analogues of the summations ε_{a <n ≤b} 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.

Vivek V Rane¹

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

Published

August 2003

Manuscript received

2 February 2002

Manuscript revised

20 January 2003