The Hurwitz and the Lerch Zeta- Functions in the Second Variable

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.