Read e-book online Basic Hypergeometric Series, Second Edition (Encyclopedia of PDF

By George Gasper, Mizan Rahman

ISBN-10: 0511526253

ISBN-13: 9780511526251

ISBN-10: 0521833574

ISBN-13: 9780521833578

This up-to-date variation will proceed to satisfy the desires for an authoritative complete research of the swiftly starting to be box of easy hypergeometric sequence, or q-series. It comprises deductive proofs, workouts, and necessary appendices. 3 new chapters were additional to this version masking q-series in and extra variables: linear- and bilinear-generating features for uncomplicated orthogonal polynomials; and summation and transformation formulation for elliptic hypergeometric sequence. furthermore, the textual content and bibliography were increased to mirror contemporary advancements. First variation Hb (1990): 0-521-35049-2

Show description

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

Similar mathematics books

Read e-book online The Everything Guide to Calculus I: A step by step guide to PDF

Calculus is the foundation of all complicated technological know-how and math. however it may be very intimidating, specially if you're studying it for the 1st time! If discovering derivatives or realizing integrals has you stumped, this publication can advisor you thru it. This essential source bargains hundreds of thousands of perform routines and covers the entire key innovations of calculus, together with: Limits of a functionality Derivatives of a functionality Monomials and polynomials Calculating maxima and minima Logarithmic differentials Integrals discovering the quantity of irregularly formed gadgets through breaking down difficult options and providing transparent motives, you'll solidify your wisdom base--and face calculus with no worry!

Get Sobolev Spaces in Mathematics II: Applications in Analysis PDF

Sobolev areas turn into the validated and common language of partial differential equations and mathematical research. between an enormous number of difficulties the place Sobolev areas are used, the next very important subject matters are within the concentration of this quantity: boundary worth difficulties in domain names with singularities, better order partial differential equations, neighborhood polynomial approximations, inequalities in Sobolev-Lorentz areas, functionality areas in mobile domain names, the spectrum of a Schrodinger operator with adverse power and different spectral difficulties, standards for the whole integrability of platforms of differential equations with purposes to differential geometry, a few elements of differential types on Riemannian manifolds on the topic of Sobolev inequalities, Brownian movement on a Cartan-Hadamard manifold, and so on.

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

Sample text

A different characterization of fq is presented in Kairies and Muldoon [1982]. 27 Other formulas involving q-Bessel functions are contained in Jackson [1904a-d, 1908], Ismail and Muldoon [1988], Rahman [1987, 1988c, 1989b,c], and Swarttouw and Meijer [1994]. It was pointed out by Ismail in an unpublished preprint in 1999 (rewritten for publication as Ismail [2003c]) that J~3) (x; q) was actually introduced by Jackson [1905a], contrary to the claim in Swarttouw [1992] that a special case of it was first discovered by Hahn [1953] and then in full generality by Exton [1978].

Br)m r where, as usual, it is assumed that none of the factors in the denominators of the terms of the series is zero. , if Re( -a) > ml + ... 1) that F [a, r+1 r b+b l ml , ... , br b 1, ... , r + mr , . 1] - 0 - , Re (-a) > ml + ... 3) These formulas are particularly useful for evaluating sums that appear as solutions to some problems in theoretical physics such as the Racah coefficients. They were also used by Gasper [1981b] to prove the orthogonality on (0,27f) of certain functions that arose in Greiner's [1980] work on spherical harmonics on the Heisenberg group.

4) The bilateral q-integral is defined by 1 00 f(t) dqt = (1 - q) f n= -00 [f(qn) + f( _qn)] qn. 5) when restricted. 14) that 1 f is suitably t x-I ((tq; q)oo ) dqt, R ex> 0 , y r--I- 0 ,- 1,- 2, ... , tqY;qoo which clearly approaches the beta function integral B q(x, y ) = 1 o B(x, y) = 11 t x - 1 (1 - t)y-l dt, Re x, Re y > 0, (1117) .. 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.

Download PDF sample

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


by Paul
4.4

Rated 4.28 of 5 – based on 24 votes