Analogues of Euler and Poisson Summation Formulae

Proceedings Mathematical Sciences

Vivek V Rane¹ 

[1] Department of Mathematics, The Institute of Science, , Madam Cama Road, Mumbai 00 0, India$$

关键词: Abel’s summation formula;    Euler summation formula;    Euler–Maclaurin summation formula;    Poisson’s summation formula;    Fourier series.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Euler–Maclaurin and Poisson analogues of the summations $sum_{a < n ≤ b}𝜒(n)f(n), sum_{a < n ≤ b}d(n) f(n), sum_{a < n ≤ b}d(n)𝜒(n) f(n)$ 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.

【 授权许可】

Unknown