A Survey for Generalized Trigonometric and Hyperbolic Functions
نویسندگان
چکیده
The generalized trigonometric functions which have a short history, were introduced by Lindqvist two decades ago. Since 2010, many mathematician began to study their classical inequalities, general convexity and concavity, multiple-angle formulas and parameter convexity and concavity. A number of results have been obtained. This is a survey. Some new refinements, generalizations, applications, and related problems are summarized.
منابع مشابه
INTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS
In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.
متن کاملInequalities involving generalized trigonometric and hyperbolic functions
The Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established. The first and the second inequalities of Huygens and Wilker, for classes of functions under discussion, are also investigated.
متن کاملar X iv : m at h / 06 07 25 0 v 1 [ m at h . C A ] 1 1 Ju l 2 00 6 PROPERTIES OF GENERALIZED UNIVARIATE HYPERGEOMETRIC FUNCTIONS
Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeomet-ric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E 7 (ellip-tic, hyperbolic) and of type E 6...
متن کاملSome Wilker and Cusa type inequalities for generalized trigonometric and hyperbolic functions
The authors obtain some Wilker and Cusa type inequalities for generalized trigonometric and hyperbolic functions and generalize some known inequalities.
متن کاملApproximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling
In this paper, we present algorithms for the approximation of multivariate periodic functions by trigonometric polynomials. The approximation is based on sampling of multivariate functions on rank-1 lattices. To this end, we study the approximation of periodic functions of a certain smoothness. Our considerations include functions from periodic Sobolev spaces of generalized mixed smoothness. Re...
متن کامل