特殊関数入門（テキスト） An Introduction to Special Functions (La Matematica per il 3+2)

Viola, Carlo

Springer International Publishing AG（2016/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 168 p.
• 商品コード 9783319413440

Full Description

The subjects treated in this book have been especially chosen to represent a bridge connecting the content of a first course on the elementary theory of analytic functions with a rigorous treatment of some of the most important special functions: the Euler gamma function, the Gauss hypergeometric function, and the Kummer confluent hypergeometric function. Such special functions are indispensable tools in "higher calculus" and are frequently encountered in almost all branches of pure and applied mathematics. The only knowledge assumed on the part of the reader is an understanding of basic concepts to the level of an elementary course covering the residue theorem, Cauchy's integral formula, the Taylor and Laurent series expansions, poles and essential singularities, branch points, etc. The book addresses the needs of advanced undergraduate and graduate students in mathematics or physics.

Contents

1 Picard's Theorems.- 2 The Weierstrass Factorization Theorem.- 3 Entire Functions of Finite Order.- 4 Bernoulli Numbers and Polynomials.- 5 Summation Formulae.- 6 The Euler Gamma-Function.- 7 Linear Differential Equations.- 8 Hypergeometric Functions.