In chapter I known asymptotic forms and expansions of the hypergeometric function obtained by Erdélyi [5], Hapaev [10,11], Knottnerus [15L Sommerfeld [25] and Watson [28] are discussed. Also the asymptotic expansions of the hypergeometric function occurring in gas-flow theory will be discussed. These expansions were obtained by Cherry [1,2], Lighthill [17] and Seifert [2J]. Moreover, using a paper by Thorne [28] asymptotic expansions of ₂F₁(p+1, -p; 1-m; (1-t)/2), -1 < t < 1, and ₂P₁( (p+m+2)/2, (p+m+1)/2; p+ 3/2-, t⁻² ), t > 1, are obtained as p-»» and m = -(p+ 1/2)a, where a is fixed and 0 < a < 1. The : expansions are in terms of Airy functions of the first kind. The hypergeometric equation is normalized in chapter II. It readily yields the two turning points t₁, i = 1,2. If we consider,the case the a=b is a large real parameter of the hypergeometric function ₂F₁(a,b; c; t), then the turning points coalesce with the regular singularities t = 0 and t = ∞ of the hypergeometric equation as | a | →∞. In chapter III new asymptotic forms are found for this particular case; that is, for ₂F₁ (a, a; c;t) , 0 < T₁ ≤ t < 1, and ₂F₁ (a,a+1-c; 1; t⁻¹), 1 < t ≤ T₂ < ∞ , as –a → ∞ . The asymptotic form is in terms of modified Bessel functions of order 1/2. Asymptotic expansions can be obtained in a similar manner. Furthermore, a new asymptotic form is derived for ₂F₁ (c-a, c-a; c; t), 0 < T₁ ≤ t < 1, as –a → ∞, this result then leads to a sharper estimate on the modulus of n-th order derivatives of holomorphic functions as n becomes large. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis deals with the properties of the coefficients of Hypergeometric Series. Specifically, we are interested in which primes appear in the denominators to a bounded power. The first main result gives a method of categorizing the primes up to equivalence class which appear finitely many times in the denominators of generalized hypergeometric series nFm over the rational numbers. Necessary and sufficient conditions for when the density is zero are provided as well as a categorization of the n and m for which the problem is interesting. The second main result is a similar condition for the appearance of primes in the denominators of the hypergeometric series 2F1 over number fields, specifically quadratic extensions Q(D). A novel conjecture to the study of p-adic numbers is also provided, which discusses the digits of irrational algebraic numbers' p-adic expansions. / Thesis / Master of Science (MSc)

ix, 147 leaves / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.) from the Dept. of Statistics, University of Adelaide, 1971

Thesis (Ph.D.) from the Dept. of Statistics, University of Adelaide, 1971.

Thesis (M.Sc.) - Carleton University, 2003. / Includes bibliographical references (p. 59-60). Also available in electronic format on the Internet.

Thesis--University of Michigan. / "Presented to the American Mathematical Society, Chicago, April 10, 1936." Includes bibliographical references (p. 21).

Thesis--University of Michigan. / "Presented to the American Mathematical Society, Chicago, April 10, 1936." Includes bibliographical references (p. 21).

Thesis (doctoral)--Friedrich-Wilhelms-Universität Berlin, 1874. / Vita.

Thesis (Ph. D.)--Washington State University, May 2010. / Title from PDF title page (viewed on June 9, 2010). "Department of Mathematics." Includes bibliographical references (p. 232-240).

Our focus, in this thesis, is on zeros of hypergeometric polynomials. Several problems in various areas of science can be seen in terms of the search of zeros of functions; and this search can be reduced to finding the zeros of approximating polynomials, since under some conditions, functions can be approximated by polynomials. In this thesis, we consider the zeros of a specific polynomial, namely the hypergeometric polynomial. We review some work done on the zero location and the asymptotic zero distribution of Gauss hypergeometric polynomials with real parameters. We extend some contiguous relations of 2F1 functions, and then we deduce the zero location for some classes of Gauss polynomials with non-real parameters. We study the asymptotic zero distribution of some classes of 3F2polynomials that extend results in the literature. / Dissertation (MSc (Applied Mathematics))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / MSc / unrestricted