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Showing 1 to 20 of 38 for “"hypergeometric"”.
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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 …
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The physical applications of hypergeometric functions
Thesis (M.S.) Massachusetts Institute of Technology. Dept. of Mathematics, 1946.
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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.
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Definite integration using the generalized hypergeometric functions.
Thesis. 1977. M.S.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
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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 …
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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 …
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On Cranks of Partitions, Generalized Lambert Series, and Basic Hypergeometric Series
… apply the same method used in Chapter 3 on basic hypergeometric series. In Chapter 4, we present a new proof of Ramanujan's 10, summation formula. And finally, in Chapter 5, we present a new proof of a general transformation formula for basic hypergeometric series that was discovered by D. B. …
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Integral Representations of the Confluent Hypergeometric Function of the Second Kind
Made available in DSpace on 2014-12-11T18:23:36Z (GMT). No. of bitstreams: 1 7114710.pdf: 1390206 bytes, checksum: 1c2e61582688b9fa99ede6f61c5abeb2 (MD5) Previous issue date: 1970
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Exploring the Plasmodium falciparum Transcriptome Using Hypergeometric Analysis of Time Series (HATS)
… We also offer a robust computational tool, Hypergeometric Analysis of Time Series (HATS), to handle challenging biological questions related to comparison of time series experiments. Our pipeline provides a rigorous method for aligning expression experiments and then determining which genes …
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Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues
… 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, and then use the method to obtain new identities and relate them to two of Ramanujan's identities. We next prove …
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ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΚΑΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ POLYA ΚΑΙ ΑΝΑΣΤΡΟΦΗ POLYA ΤΑΞΕΩΣ Κ
… THE FOLLOWING DISTRIBUTIONS OF ORDER K, TYPE II: HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA, INVERSE POLYA AND UNIFORM DISTRIBUTION OF ORDER K ON THE INTEGERS 1,....,K. WE DERIVE THE MOMENT GENERATING FUNCTIONS, MEANS AND VARIANCES OF …
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Uses of the Hypergeometric Distribution for Determining Survival or Complete Representation of Subpopulations in Sequential Sampling
<p>This thesis will explore the hypergeometric probability distribution by looking at many different aspects of the distribution. These include, and are not limited to: history and origin, derivation and elementary applications, properties, relationships to other probability models, kindred …
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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 …
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Generalizations of Certain Results on Continued Fraction
… of the quotient of two contiguous basic hypergeometric function in arbitrarily many variables as a G-continued fraction. A careful interpretation of convergence is given for different cases of this expansion. When a full vector space of solutions of a q-difference equation is known, we …
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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 …
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Quantum intertwiners and integrable systems
… type integral formula for Heckman- Opdam hypergeometric functions. This formula is related to an integral formula appearing in recent work of Borodin-Gorin by integration over Liouville tori of the Gelfand-Tsetlin integrable system. At the quantum level, we obtain a new proof of the …
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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 …
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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.
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The propagator for graviton modes in supergravity on ADS5 x S5
… of three of these functions is a certain hypergeometric function.
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