Analogues of Euler and Poisson summation formulae
Rane, Vivek V
Original · EN
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.
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