Analogues of Euler and Poisson summation formulae |
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Authors: | Vivek V Rane |
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Institution: | (1) Department of Mathematics, The Institute of Science, 15, Madam Cama Road, 400 032 Mumbai, India |
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Abstract: | 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. |
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Keywords: | Abel’ s summation formula Euler summation formula Euler-Maclaurin summation formula Poisson’ s summation formula Fourier series |
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