5 papers
Gamma,Psi,Bernoulli Functions via Hurwitz Zeta Function
Vivek V. Rane
Using three basic facts concerning Hurwitz zeta function,we give new natural proofs of the known results on Bernoulli polynomials,gamma function and also obtain Gauss' expression f…
Divisor Problem and an Analogue of Euler's Summation Formula
Vivek V. Rane
By simple elementary method,we obtain with ease,a highly simple expression for the remainder term of the divisor problem and use it to obtain an Euler-Maclaurin analogue of summati…
Fourier Series Of the Derivatives of Hurwitz and Lerch Zeta Functions
Vivek V. Rane
As a function of second variable, we identify the Fourier series of Hurwitz zeta function and its derivatives on the unit interval. Consequently, we obtain results based on the for…
Instant Evaluation and Demystification of zeta(n),L(n,chi) that Euler,Ramanujan Missed III
Vivek V. Rane
We show that for a non-positive value of the first variable,Hurwitz zeta function becomes a polynomial in the second variable. We show this, using 'integration approach', instead o…
Instant Evaluation and Demystification of zeta(n),L(n,chi) that Euler,Ramanujan Missed - II
Vivek V. Rane
For Hurwitz zeta function, we obtain power series expression in second variable for its higher order derivatives (with respect to first variable) at non-positive integer arguments…