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＜電子ブック＞
Second Order Differential Equations : Special Functions and Their Classification / by Gerhard Kristensson

版	1st ed. 2010.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2010
大きさ	XII, 219 p : online resource
著者標目	*Kristensson, Gerhard author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Special functions LCSH:Functions of complex variables LCSH:Difference equations LCSH:Functional equations FREE:Differential Equations FREE:Special Functions FREE:Functions of a Complex Variable FREE:Difference and Functional Equations
一般注記	Basic properties of the solutions -- Equations of Fuchsian type -- Equations with one to four regular singular points -- The hypergeometric differential equation -- Legendre functions and related functions -- Confluent hypergeometric functions -- Heun’s differential equation Second Order Differential Equations presents a classical piece of theory concerning hypergeometric special functions as solutions of second-order linear differential equations. The theory is presented in an entirely self-contained way, starting with an introduction of the solution of the second-order differential equations and then focusingon the systematic treatment and classification of these solutions. Each chapter contains a set of problems which help reinforce the theory. Some of the preliminaries are covered in appendices at the end of the book, one of which provides an introduction to Poincaré-Perron theory, and the appendix also contains a new way of analyzing the asymptomatic behavior of solutions of differential equations. This textbook is appropriate for advanced undergraduate and graduate students in Mathematics, Physics, and Engineering interested in Ordinary and Partial Differntial Equations. A solutions manual is available online HTTP:URL=https://doi.org/10.1007/978-1-4419-7020-6

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