Thesis (Ph. D.)--Ohio State University, 1987. / Includes bibliographical references (leaves 143-149). Available online via OhioLINK's ETD Center

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Thesis (PH. D.) - University of Michigan. / Reprinted from Duke mathematical journal, vol. 4, no. 3, September, 1938.

The evaluation of infinite series plays an important part in numerical calculation. In hand calculation whenever a transcendental function is involved, one usually consults a table. Not only do the construction of the tables require the evaluation of transcendental functions, but with the advent of the electronic computer it is usually more convenient to have such evaluation carried out by the computer than to try to store a table of the necessary values to carry out the intended calculation. / Advisor: H. C. Griffith, Professor Directing Study. / Typescript. / "August 1960." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 37).

"The purpose of this paper is to study methods by which a value can be assigned to an infinite series. The reason for studying about these methods lies in the fact that infinite series often appear as the end result of a calculation or computation. A desire to obtain a usable end result leads us to the investigation of methods for evaluating infinite series"--Introduction. / "August, 1955." / Typescript. / Advisor: Howard E. Taylor, Professor Directing Paper. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 40).

The purpose of this paper is to examine certain questions concerning infinite series. The first chapter introduces several basic definitions and theorems from calculus. In particular, this chapter contains the proofs for various convergence tests for series of real numbers. The second chapter deals primarily with the equivalence of absolute convergence, unconditional convergence, bounded multiplier convergence, and c0 multiplier convergence for series of real numbers. Also included in this chapter is a proof that an unconditionally convergent series may be rearranged so that it converges to any real number desired. The third chapter contains a proof of the Silverman-Toeplitz Theorem together with several applications.

In 1943 R. C. Buck showed that a sequence x is convergent if some regular matrix sums every subsequence of x. Thus, for example, if every subsequence of x is Cesaro summable, then x is actually convergent. Buck's result was quite surprising, since research in summability theory up to that time gave no hint of such a remarkable theorem. The appearance of Buck's result in the Bulletin of the American Mathematical Society (3) created immediate interest and has prompted considerable research which has taken the following directions: (i) to study regular matrix transformations in order to shed light on Buck's theorem, (ii) to extend Buck's theorem, (iii) to obtain analogs of Buck's theorem for sequence spaces other than the space of convergent sequences, and (iv) to obtain analogs of Buck's theorem involving processes other than subsequencing, such as stretching. The purpose of the present paper is to contribute to all facets of the problem, particularly to (i), (iii), and (iv).

This thesis attempts to establish properties of Hölder and Cesàro summable series analogous to those of ordinary convergent series and also to establish properties that are possibly different from those of convergent series.

Thesis (M. Sc.)--Carleton University, 2005. / Includes bibliographical references (p. 111-114). Also available in electronic format on the Internet.