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A new method in the study of Euler sums
Authors:Ankur Basu
Institution:(1) C/o Ranjit Basu, 82A Ramprasad Chatterjee Road, Narua, P.O., Chandannagar, Dist. Hooghly, 712136, West Bengal, India
Abstract:A new method in the study of Euler sums is developed. A host of Euler sums, typically of the form $\sum_{n=1}^{\infty}\frac{f(n)}{n^{s}}\sum_{m=1}^{n}\frac{g(m)}{m^{t}}$ , are expressed in closed form. Also obtained as a by-product, are some striking recursive identities involving several Dirichlet series including the well-known Riemann Zeta-function.
Keywords:Riemann Zeta function  Euler sums  Recursions formulas
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