Basic Hypergeometric Series, Second Edition (Encyclopedia of by George Gasper, Mizan Rahman PDF

By George Gasper, Mizan Rahman

ISBN-10: 0511526253

ISBN-13: 9780511526251

ISBN-10: 0521833574

ISBN-13: 9780521833578

This up to date version will proceed to fulfill the desires for an authoritative finished research of the quickly growing to be box of uncomplicated hypergeometric sequence, or q-series. It comprises deductive proofs, workouts, and beneficial appendices. 3 new chapters were further to this variation overlaying q-series in and extra variables: linear- and bilinear-generating capabilities for uncomplicated orthogonal polynomials; and summation and transformation formulation for elliptic hypergeometric sequence. furthermore, the textual content and bibliography were extended to mirror fresh advancements. First version Hb (1990): 0-521-35049-2

Show description

Read or Download Basic Hypergeometric Series, Second Edition (Encyclopedia of Mathematics and its Applications) PDF

Similar mathematics books

Operator Theoretic Aspects of Ergodic Theory (Graduate Texts by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel PDF

Attractive contemporary effects through Host–Kra, Green–Tao, and others, spotlight the timeliness of this systematic advent to classical ergodic thought utilizing the instruments of operator concept. Assuming no earlier publicity to ergodic conception, this e-book offers a contemporary beginning for introductory classes on ergodic concept, particularly for college students or researchers with an curiosity in useful research.

Computer methods for ODEs and differential-algebraic - download pdf or read online

Designed for these those who are looking to achieve a pragmatic wisdom of contemporary ideas, this ebook includes all of the fabric worthwhile for a direction at the numerical resolution of differential equations. Written via of the field's major gurus, it presents a unified presentation of preliminary worth and boundary price difficulties in ODEs in addition to differential-algebraic equations.

Halmos. Finite-dimensional vector spaces. Springer - download pdf or read online

"The concept is systematically constructed by way of the axiomatic procedure that has, due to the fact that von Neumann, ruled the overall method of linear useful research and that achieves right here a excessive measure of lucidity and readability. The presentation is rarely awkward or dry, because it occasionally is in different "modern" textbooks; it really is as unconventional as one has come to count on from the writer.

Additional resources for Basic Hypergeometric Series, Second Edition (Encyclopedia of Mathematics and its Applications)

Sample text

2) q ,q ,q 00 q 1/( 1/-1) . 27 Show that 00 n= -CX) 00 Both of these are q-analogues of the generating function 00 L n= t n In(x) = ex (t-C 1 )/2. J( )( ) e , k= 0 q; q k q; q n-k where x = cos B; see Szego [1926]' Carlitz [1955, 1957a, 1958, 1960] and Rogers [1894, 1917]. Derive the generating function n f:'~o Hn(xlq) (q; q)n t 1 = (teiIJ, te-iIJ; q)oo' It I < 1. 29 The continuous q-ultraspherical polynomials are defined in Askey and Ismail [1983] by C ( . J n=O n = ((3te iIJ , (3te- iIJ ; q)oo ( ·IJ -"IJ) te' te ' .

2) (Zq2; q)oo. 8) n= 1 in terms of infinite products. 11) n= 1 and 00 194 (X, q) = II (1- q2n)(1_ 2q2n-1 cos2x + q4n-2). 12) n= 1 It is common to write 19 k (x) for 19 k (x, q), k = 1, ... ,4. 13) one can think of the theta functions 19 1 (x, q) and 192 (x, q) as one-parameter deformations (generalizations) of the trigonometric functions sin x and cos x, 1. 7 q-Saalschutz formula 17 respectively. 14) is never zero. 9) it is clear that [a; CT, T] is well-defined, [-a; CT, T] = -[a;CT,TJ, [1;CT,T] = 1, and .

8) 24 Basic hypergeometric series as q ----+ 1-. 1) in the q-integral form 2¢1 ) _ fq(c) ( a b. c. 10) where Iarg(l- z)1 < 7r and Re c> Re b > O. The q-integral notation is, as we shall see later, quite useful in simplifying and manipulating various formulas involving sums of series. ;q)n' (a; q)n(qja; q)-n = (-atq(~), (q, -q, _q2; q2)cx; = 1. 2 The q-binomial coefficient is defined by [n] (q;q)n k q - (q; q)k(q; q)n-k for k = 0,1, ... 3+ I; q)cx; (q, q<>+ I; q)cx; for complex a and f3 when Iql (i) (ii) (iii) (q<>+ I; q)k (q;q)k ' < 1.

Download PDF sample

Basic Hypergeometric Series, Second Edition (Encyclopedia of Mathematics and its Applications) by George Gasper, Mizan Rahman


by Ronald
4.0

Rated 4.87 of 5 – based on 35 votes