By H. M. Srivastava

Zeta and q-Zeta capabilities and linked sequence and Integrals is a completely revised, enlarged and up-to-date model of sequence linked to the Zeta and comparable services. some of the chapters and sections of the ebook were considerably changed or rewritten and a brand new bankruptcy at the thought and functions of the elemental (or q-) extensions of varied exact services is integrated. This booklet can be useful because it covers not just precise and systematic shows of the speculation and purposes of many of the tools and strategies utilized in facing many alternative sessions of sequence and integrals linked to the Zeta and comparable services yet stimulating ancient money owed of a big variety of difficulties and well-classified tables of sequence and integrals.Detailed and systematic shows of the speculation and purposes of a few of the tools and methods utilized in facing many various periods of sequence and integrals linked to the Zeta and similar features

**Read Online or Download Zeta and q-Zeta Functions and Associated Series and Integrals (Elsevier Insights) PDF**

**Best general & reference books**

**Colour Chemistry (Rsc Paperbacks)**

This e-book offers an up to date perception into the chemistry in the back of the color of the dyes and pigments that make our global so vibrant. The remarkable breadth of assurance starts off with a dip into the historical past of color technology. "Colour Chemistry" then is going directly to examine the constitution and synthesis of many of the dyes and pigments, besides their purposes within the conventional components of textiles, coatings and plastics, and in addition the ever-expanding variety of "high-tech" purposes.

**Absorption. Fundamentals & Applications**

This e-book offers a realistic account of the fashionable concept of calculation of absorbers for binary and multicomponent actual absorption and absorption with simultaneous chemical response. The publication comprises elements: the speculation of absorption and the calculation of absorbers. half I covers uncomplicated wisdom on diffusion and the idea of mass move in binary and multicomponent structures.

**An Introduction to the Mechanical Properties of Solid Polymers**

Presents a finished advent to the mechanical behaviour of strong polymers. widely revised and up to date all through, the second one variation now comprises new fabric on mechanical relaxations and anisotropy, composites modelling, non-linear viscoelasticity, yield behaviour and fracture of tricky polymers.

**Non-wettable surfaces: theory, preparation and applications**

The target of this publication is to combine information regarding the speculation, coaching and functions of non-wettable surfaces in a single quantity. via combining the dialogue of all 3 features jointly the editors will convey how idea assists the improvement of arrangements equipment and the way those surfaces could be utilized to diversified occasions.

- Chemistry in the National Science Education Standards: Models for Meaningful Learning in the High School Chemistry Classroom
- Lead 68. Edited Proceedings, Third International Conference on Lead, Venice
- Molecular Theory of Capillarity
- Cloud Connections: Build Your Foundation to the On-premise Cloud
- Phase Transfer Catalysis. Principles and Techniques
- Chemical Reactions Their Theory and Mechanism

**Additional info for Zeta and q-Zeta Functions and Associated Series and Integrals (Elsevier Insights) **

**Example text**

5 1 in (20), and using (6) and (8), we obtain 2 1 3 G 4 4 1 1 3 9 = 2− 4 ·π − 2 · e 8 · A− 2 . 848718 · · · . (24) It follows from (23), (24) and (6) that G G 3 4 5 4 1 1 G = 2− 8 · π − 4 · e 2π . (25) Introduction and Preliminaries 45 Integral Formulas Involving the Double Gamma Function We begin by recalling the following integral formula: z πt cot π t dt = z log(2π) + log 0 G(1 − z) , G(1 + z) (26) which is due, originally, to Kinkelin [666]. Indeed, in view of (3), if we set (z) := G(1 + z) = (2π)z e−z G(1 − z) ∞ k=1 1 + kz 1 − kz k e−2z and differentiate logarithmically with respect to z, and apply the known expansion (see Ahlfors [13, p.

Some simple consequences of Kinkelin’s formula (26) are worthy of note here (see also Barnes [94, p. 279]). First, by using integration by parts in (26), we have z log sin πt dt = z log 0 which, upon setting t = z 1 2 sin πz G(1 + z) + log , 2π G(1 − z) − u and replacing z by 1 2 (28) − z, yields cos π z 1 1 log − log 2 − log log cos π t dt = z − 2 2π 2 0 G 1 − z + log 2 G 1 2 +z 1 2 −z . (29) Making use of (29), we obtain the following analogue of (26): z 0 1 cos πz π t tan πt dt = − log − z log(2π) − log 2 π G 1 − z + log 2 G 1 2 +z 1 2 −z , (30) 46 Zeta and q-Zeta Functions and Associated Series and Integrals which would follow also from (26) by setting t = 12 − u and replacing z by Combining (28) and (29), we readily have the integral formula: z log tan πt dt = z log tan πz + 0 1 cos π z log + log 2 π G G (1 + z) + log − log G (1 − z) G 1 2 +z 1 2 −z 1 2 − z.

269]) that G (z + 1)/G(z + 1) is the only solution of f (z + 1) = f (z) + (z) , (z) which has such an asymptotic expansion near at infinity. 3(58), reduces at once to (n + 1) log n − n + z (log n + 1 + γ − 2β) + 1 − α + O n−1 2 (n → ∞), which, upon putting α= 1 1 1+γ − log (2π) and β = , 2 2 2 becomes the right-hand side of (7). (12) Introduction and Preliminaries 43 If we now substitute the values of α and β from (12) into (10), we obtain the following expression: − G (z + 1) 1 1 = − log(2π) + (1 + γ ) z G(z + 1) 2 2 + d log dz ∞ k=0 1 (z + 1 + k) exp −z ψ(1 + k) − z2 ψ (1 + k) (1 + k) 2 (|z| < 1; z ∈ C), which, upon integrating with respect to z and obtaining the value of the constant of integration by making z = 0, finally yields the desired expression (4) valid for |z| < 1.