AMS Chelsea Publishing 1960; 342 pp; hardcover Volume: 143 ISBN10: 0828401438 ISBN13: 9780828401432 List Price: US$44 Member Price: US$39.60 Order Code: CHEL/143
 This book is based on several courses taught by the author at the University of Michigan between 1908 and 1912. It covers two main topics: asymptotic series and the theory of summability. The discussion of nowhere convergent asymptotic series includes the socalled MacLaurent summation formula, determining asymptotic expansions of various classes of functions, and the study of asymptotic solutions of linear ordinary differential equations. On the second topic, the author discusses various approaches to the summability of divergent series and considers in detail applications to Fourier series. Readership Graduate students and research mathematicians. Table of Contents Studies on Divergent Series and Summability  The MacLaurin sumformula, with introduction to the study of asymptotic series
 The determination of the asymptotic developments of a given function
 The asymptotic solutions of linear differential equations
 Elementary studies on the summability of series
 The summability and convergence of Fourier series and allied developments
 Appendix
 Bibliography
The Asymptotic Developments of Functions Defined by MacLaurin Series  Preliminary considerations. First general theorem
 The theorem of Barnes
 MacLaurin series whose general coefficient is algebraic in character
 Second general theorem
 Auxiliary theorems
 MacLaurin series whose general coefficient involves the reciprocal of a single gamma function; Functions of exponential type
 MacLaurin series whose general coefficient involves the reciprocal of the product of two gamma functions; Functions of Bessel type
 Determination of the asymptotic behavior of the solutions of differential equations of the Fuchsian type
 Bibliography
