The Hurwitz and the Lerch Zeta-Functions in the Second Variable deals with Hurwitz’s zeta-function as a function of the second variable, using elementary methods. In parallel, briefly Lerch’s zeta-function as the function of the second variable has been developed. Hurwitz’s zeta-function as a function of the second polynomials, gamma/digamma functions, Dirichlet L-series, multiple zeta functions etc. The pre-requisites for this book are a knowledge of advanced calculus, function theory of one complex variable with a brief exposure to arithmetical functions, Riemann’s zeta function and Dirichlet L-series.

Notations and Definitions / Preface, Intent and Introduction / Known Facts about the Functions under consideration, in brief / On Riemann-Stieltjes Integration, in brief / Abbreviated Form of Power Series of ? (s,?) and allied Trigonometric-type Functions / 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 ?? r?? (s,?) / Instant Evaluation and Demystification of ?(n), L(n,??) that Euler, Ramanujan Missed-I / Instant Evaluation and Demystification of ?(n), L(n,??) that Euler, Ramanujan Missed-II / Instant Evaluation and Demystification of ?(n), L(n,??) 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 ?-Calculus-cum-?-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 the Divisor Problem.

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