The Hurwitz and the Lerch Zeta-functions in the second variable

Includes bibliographical references.

Chapter 0: Generalised Euler's Summation Formula and the Basic Fourier Series Chapter 1: Analogues of Euler and Poisson Summation Formulae Chapter 2: Classical Theory of Fourier Series: Demystified and Generalised Chapter 3: Dirichlet L-function and Power Series for Hurwitz Zeta Function Chapter 4: Precise Definition and Analyticity of i i ri i (s, i !) Chapter 5: Instant Evaluation and Demystification of i (n), L(n, i i GBP) that Euler, Ramanujan Missed-I Chapter 6: Instant Evaluation and Demystification of i (n), L(n, i GBP) that Euler, Ramanujan Missed-II Chapter 7: Instant Evaluation and Demystification of i (n), L(n, i i GBP) that Euler, Ramanujan Missed-III Chapter 8: Instant Multiple Zeta Values at Non-positive Integers and the Bernoulli Polynomials Chapter 9: Gamma, Psi, Bernoulli Functions via Hurwitz Zeta Function / The i !-Calculus-cum-i !-Analysis of Chapter 10: Integral Expressions for and Approximations

The Hurwitz and the Lerch Zeta- Functions in the Second Variable, which is based on author's own research work, mainly deals with the study of the Hurwitz zeta Function as a function of the second variable, thereby connecting Riemann zeta function, gamma function, Bernoulli polynomials, Dirichlet L-Series and many other functions. In this book, the author has developed an approach based on Euler's summation fornula-cum-the basic fourier series, to deal with problems in number theory. In particular, the book gives a new approach to classical fourier theory. The book uses classical elementary methods subtly. Also the calculus of the Hurwitz zeta function as a function of the second variable has been developed.