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Full Description
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.
Contents
Notations and Definitions / Preface, Intent and Introduction / Known Facts about the Functions under consideration, in brief / on Riemann-Stieltjes Integration, in brief / Chapterwise Summary of Results / Generalised Euler's Summation Formula and the Basic Fourier Series / Analogues of Euler and Poisson Summation Formulae / Classical Theory of Fourier Series: Demystified and Generalised / Dirichlet L-function and Power Series for Hurwitz Zeta Function / Precise Definition and Analyticity of i i ri i (s,i !) / Instant Evaluation and Demystification of i (n), L(n,i i GBP) that Euler, Ramanujan Missed-I / Instant Evaluation and Demystification of i (n), L(n,i i GBP) that Euler, Ramanujan Missed-II / Instant Evaluation and Demystification of i (n), L(n,i i GBP) that Euler, Ramanujan Missed-III / Instant Multiple Zeta Values at Non-positive Integers and the Bernoulli Polynomials / Gamma, Psi, Bernoulli Functions via Hurwitz Zeta Function / The i !-Calculus-cum-i !-Analysis of / Integral Expressions for and Approximations / Demystification of Taylor , Laurent Coefficients of Lerch , Hurwitz Zeta Functions / Fourier Series of the Derivatives of Hurwitz and Lerch Zeta Functions / Exact and Approximate Functional Equations of Lerch's Zeta Function / On an Approximate Functional Equation for Dirichlet L-series / Approximate Functional Equation for the Product of Functions and Divisor Problem.
