28 research outputs found
Generalised cosine functions, basis and regularity properties
We examine regularity and basis properties of the family of rescaled
-cosine functions. We find sharp estimates for their Fourier coefficients.
We then determine two thresholds, , such that this family is
a Schauder basis of for all and .Comment: 24 page
Geometric convexity of the generalized sine and the generalized hyperbolic sine
In the paper, the authors prove that the generalized sine function
and the generalized hyperbolic sine function
are geometrically concave and geometrically convex, respectively. Consequently,
the authors verify a conjecture posed in the paper "B. A. Bhayo and M.
Vuorinen, On generalized trigonometric functions with two parameters, J.
Approx. Theory 164 (2012), no.~10, 1415\nobreakdash--1426; Available online at
\url{http://dx.doi.org/10.1016/j.jat.2012.06.003}".Comment: 5 page
Logarithmic mean inequality for generalized trigonometric and hyperbolic functions
In this paper we study the convexity and concavity properties of generalized
trigonometric and hyperbolic functions in case of Logarithmic mean.Comment:
On generalized trigonometric functions and series of rational functions
Here we introduce a way to construct generalized trigonometric functions
associated with any complex polynomials, and the well known trigonometric
functions can be seen to associate with polynomial . We will show that
those generalized trigonometric functions have algebraic identities which
generalizes the well known . One application of the
generalized trigonometric functions is evaluating infinite series of rational
functions.Comment: 14 page