Definite integration using the generalized hypergeometric by Ioannis Dimitrios Avgoustis

By Ioannis Dimitrios Avgoustis

Show description

Read Online or Download Definite integration using the generalized hypergeometric functions PDF

Similar geometry and topology books

Basic geometry

A hugely prompt high-school textual content through eminent students

Lectures in Projective Geometry

This quantity serves as an extension of excessive school-level reviews of geometry and algebra, and proceeds to extra complex subject matters with an axiomatic method. comprises an introductory bankruptcy on projective geometry, then explores the relatives among the fundamental theorems; higher-dimensional house; conics; coordinate platforms and linear differences; quadric surfaces; and the Jordan canonical shape.

Les Fondements de la géométrie

Approche axiomatique de l. a. géométrie
* through l. a. constitution vectorielle
* comme constitution d'incidence (à los angeles façon de Veblen & younger)

Additional info for Definite integration using the generalized hypergeometric functions

Example text

1, and the notes to Chapter 9. The primary motivations of the authors of those papers came from the investigation of the oscillatory phenomena in the geometry and the spectrum of fractal drums [Lap3] (including self-similar drums) and, in particular, of fractal strings, where the connections between direct or inverse spectral problems and the Riemann zeta function or the Riemann hypothesis were first discovered in [LapPo1, 2] or [LapMa1, 2], respectively. 17 for a sample of references in the physics literature—of which we have become aware recently and with rather different motivations, coming from the study of turbulence, lacunarity, biophysics, and other applications.

We note that such strings can no longer be realized geometrically as subsets of Euclidean space. 4 Higher-Dimensional Analogue: Fractal Sprays Fractal sprays were introduced in [LapPo3] (see also [Lap2, §4] announcing some of the results in [LapPo3]) as a natural higher-dimensional analogue of fractal strings and as a tool to explore various conjectures about the spectrum (and the geometry) of drums with fractal boundary10 in Rd . In the present book, fractal sprays and their generalizations (to be introduced later on) will continue to be a useful exploratory tool and will enable us to extend several of our results to zeta functions other than the Riemann zeta function.

17) The Geometric Zeta Function of a Fractal String ∞ ∞ Let L be a fractal string with sequence of lengths {lj }j=1 . The sum j=1 ljσ converges for σ = 1. It follows that the (generalized) Dirichlet series ∞ ljs ζL (s) = j=1 defines a holomorphic function for Re s > 1. 10 below that this series converges in the open right half-plane Re s > D, defined by the Minkowski dimension D, but that it diverges at s = D. 7) above for the definition of the multiplicity wl in the following definition. 6 Note that since p = 2π/ log 3 and u = − log ε, we have eipu = ε−ip .

Download PDF sample

Rated 4.08 of 5 – based on 26 votes