This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI 1], voi. III, chap. 19) and in TRUESDELL 1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series, Lc, . p, . (z), where {p, . } is a prescribed sequence of functions, and the connections between the function f and the coefficients c, . . BIEBERBACH's mono graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p, . (z) =z," and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M."

"Me, My Pillow and Kicking Feet" is one of those classic stories for kids that explores underlying childhood and parent-child relationship themes, but doesn't take itself too seriously. It is vividly illustrated and covers a little boy who enjoys kicking his pillows at home, down the street, in the grocery store and even at the zoo. The inspiration for the story has an interesting twist. The author is a podiatrist foot specialist who was inspired by his own children who were notorious pillow kickers. They often used their pillows for play leaving them on the floor and stepping all over them. We all know how children get into things that seem fun, but may not always be best, and there are things they may be exposed to that parents can teach them about in a caring way. The pillow kicking child's father must explain, "Pillows are for your head, not for your feet." Check it out - you'll like how the father teaches the child this lesson.

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!

This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone