Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 16 of 16 for “"hypergeometric functions"”.
-
Hypergeometric functions and Mahler measure
The logarithmic Mahler measure of an n-variable Laurent polynomial, P(x1,...,xn) is defined by [expression]. Using experimental methods, David Boyd conjectured a large number of explicit relations between Mahler measures of polynomials and special values of different types of L-series. This thesis …
-
The physical applications of hypergeometric functions
Thesis (M.S.) Massachusetts Institute of Technology. Dept. of Mathematics, 1946.
-
Feynman integrals, hypergeometric functions and nested sums
… integrals in 3 and 4 dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we implemented in FORM to expand these in terms of nested sums.
-
Definite integration using the generalized hypergeometric functions.
Thesis. 1977. M.S.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
-
Arithmetic and analytic properties of finite field hypergeometric functions
… analytic properties of Gaussian (finite field) hypergeometric series. We present expressions for the number of F,-points on certain families of varieties as special values of these functions. We also present "hypergeometric trace formulas" for the traces of Hecke operators on spaces of cusp …
-
Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues
… identities are those involving ratios of Gamma functions in Chapter 12 of his second notebook. This thesis develops a method for deriving such identities, using hypergeometric functions as the main tool. We begin by deriving a continued fraction identity, use it to prove Ramanujan's Entry 34, …
-
Topics in complex random matrices and information theory
… These distributions are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. We derive several results on complex hypergeometric functions and zonal polynomials that are used to evaluate these distributions. We also …
-
Asymptotic Formulas For Large Arguments Of Hypergeometric-type Functio
Hypergeometric type functions have a long list of applications in the field of sciences. A brief history is given of Hypergeometric functions including some of their applications. A development of a new method for finding asymptotic formulas for large arguments is given. This new method is applied …
-
Applications of continued fractions in one and more variables
… form are then derived for certain generalised hypergeometric functions using those hypergeometric functions that satisfy three-term recurrence relations and have simple continued fraction expansions. Error estimates are also given in this case. The class of corresponding sequence algorithms is …
-
A new computation of the Bergman kernel and related techniques
… a cancellation of singularities for generalized hypergeometric functions and weighted Bergman kernels. Finally, we give an alternative approach to obtain explicit bases for complex harmonic homogeneous polynomial spaces.
-
Modular equations and Ramanujan's cubic and quartic theories of theta functions
… Choi discovered in his work on basic bilateral hypergeometric series and mock theta functions. In Chapter 4, we derive new identities related to the Ramanujan-G\""{o}llnitz-Gordon continued fraction that are similar to those for the famous Rogers-Ramanujan continued fraction. We give a new proof …
-
Quantum intertwiners and integrable systems
… operators for quantum groups and eigenfunctions for quantum integrable systems. First, we study the Etingof-Kirillov Jr. expression of Macdonald polynomials as traces of intertwiners of quantum groups in the Gelfand-Tsetlin basis. In the quasiclassical limit, we obtain a new …
-
Fluid mechanics of liquid drops and thin-films
… system which yields solutions involving hypergeometric functions. The predictions show excellent agreement with experimental data reported in the literature, particular for drops with low contact angles and higher modes of vibration. The third topic is to find the underlying physics of …
-
A race toward the origin between n random walks
… in particular, in terms of Generalized Hypergeometric Functions. In addition, formulae are given for the duration of what may now be regarded as a race with winning post at the origin. In the continuous time situation, the motion of the n particles is governed by n independent Poisson …
-
Asymptotics, exact results, and analogies in p-adic random matrix theory
… complex random matrices and type A Heckman-Opdam hypergeometric functions. (2) We prove that the boundary of the Hall-Littlewood t-deformation of the Gelfand-Tsetlin graph is parametrized by infinite integer signatures, extending results of Gorin and Cuenca on boundaries of related deformed …
-
Mathematical methods in atomic physics = Métodos matemáticos en física atómica
Los problemas de dispersión de partículas, como son los de dos y tres cuerpos, tienen una relevancia crucial en física atómica, pues permiten describir diversos procesos de colisiones. Hoy en día, los casos de dos cuerpos pueden ser resueltos con el grado de precisión numérica que se desee. Los …