Thesis (doctoral)--Schlesische Friedrich-Wilhelms-Universität zu Breslau, 1919. / Cover title. Vita.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis--M. Phil., University of Hong Kong, 1979.

Not available / text

published_or_final_version / Mathematics / Master / Master of Philosophy

Proefschrift--Utrecht. / "Stellingen": [2] p. laid in.

Proefschrift--Utrecht. / "Stellingen": [2] p. laid in.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 61).

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

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.