Formulas for Powers of the Hyperbolic Tangent with an Application to Higher-Order Tangent Numbers
نویسندگان
چکیده
منابع مشابه
Higher-order tangent and secant numbers
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Tangent numbers Tangent numbers of order k Secant numbers Secant numbers of order k Higher-order (or, generalized)...
متن کاملUniversal Approximator Property of the Space of Hyperbolic Tangent Functions
In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.
متن کاملLagrangians and higher order tangent spaces
The aim of the paper is to prove that T M , the tangent space of order k ≥ 1 of a manifold M , is diffeomorphic with T 1 k M , the tangent space of k–velocities, and also with ( T 1 k )∗ M , the cotangent space of k–covelocities, via suitable Lagrangians. One prove also that a hyperregular Lagrangian of first order on M can give rise to such diffeomorphisms. M.S.C. 2000: 53C60, 53C80, 70H50.
متن کاملTangent Measure Distributions of Hyperbolic Cantor
Tangent measure distributions were introduced by Bandt 2] and Graf 8] as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by certain contractive mappings, which are not necessarily similitudes. We show that the tangent measure distributions o...
متن کاملOn the approximation order of tangent estimators
A classic problem in geometric modelling is curve interpolation to data points. Some of the existing interpolation schemes only require point data, whereas others, require higher order information, such as tangents or curvature values, in the data points. Since measured data usually lack this information, estimation of these quantities becomes necessary. Several tangent estimation methods for p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2005
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181069685