Results 31 to 40 of about 5,130,669 (296)

Continued fraction expansions for q-tangent and q-cotangent functions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2010
For 3 different versions of q-tangent resp. q-cotangent functions, we compute the continued fraction expansion explicitly, by guessing the relative quantities and proving the recursive relation afterwards.
Helmut Prodinger
doaj   +1 more source

Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$

Researches in Mathematics, 2022
Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched continued fraction expansions of the ratios of these ...
R.I. Dmytryshyn, I.-A.V. Lutsiv
doaj   +1 more source

Continued fraction approximation for the nuclear matter response function [PDF]

, 2008
We use a continued fraction approximation to calculate the RPA response function of nuclear matter. The convergence of the approximation is assessed by comparing with the numerically exact response function obtained with a typical effective finite-range ...
A. L. Fetter, D. Gogny, J. Margueron, J. Navarro, M. N. Harakeh, Nguyen Van Giai, P. Schuck   +6 more
core   +5 more sources

Ramanujan and the Regular Continued Fraction Expansion of Real Numbers [PDF]

, 2004
In some recent papers, the authors considered regular continued fractions of the form \[ [a_{0};\underbrace{a,...,a}_{m}, \underbrace{a^{2},...,a^{2}}_{m}, \underbrace{a^{3},...,a^{3}}_{m}, ...
Laughlin, James Mc, Wyshinski, Nancy J.
core   +3 more sources

Convergence criteria of branched continued fractions

Researches in Mathematics
The convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed.
I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak
doaj   +1 more source

On generalization of continued fraction of Gauss

International Journal of Mathematics and Mathematical Sciences, 1990
In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
doaj   +1 more source

Some properties of branched continued fractions of special form

Karpatsʹkì Matematičnì Publìkacìï, 2015
The fact that the values of the approximates of the positive definite branched continued fraction of special form are all in a certain circle is established for the certain conditions.
R.I. Dmytryshyn
doaj   +1 more source

Continued fraction solution of Krein's inverse problem

, 2011
The spectral data of a vibrating string are encoded in its so-called characteristic function. We consider the problem of recovering the distribution of mass along the string from its characteristic function.
Borodin A N, Boumenir A, Donati-Martin C, Dym H, Dym H, Dym H, Gantmacher F R, Kac I S, Knight F B, Stieltjes T J, Wall H S, Watanabe S, Yves Tourigny   +12 more
core   +1 more source

Numerical stability of the branched continued fraction expansion of Horn's hypergeometric function $H_4$

Matematychni Studii
In this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions.
R. Dmytryshyn, C. Cesarano, I.-A.V. Lutsiv, M. Dmytryshyn   +3 more
semanticscholar   +1 more source

Representation of Some Ratios of Horn’s Hypergeometric Functions H₇ by Continued Fractions

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Tamara Antonova, Roman Dmytryshyn, Pavlo Kril, Serhii Sharyn   +3 more
doaj   +1 more source