EuDML | Browse

MSC 2010: 33B10, 33E20Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner, we define deformed sine...

The distribution of Mahler's measures of reciprocal polynomials.

Sinclair, Christopher D. (2004)

International Journal of Mathematics and Mathematical Sciences

The evaluation of two-dimensional lattice sums via Ramanujan's theta functions

Ping Xu (2014)

Acta Arithmetica

We analyze various generalized two-dimensional lattice sums, one of which arose from the solution to a certain Poisson equation. We evaluate certain lattice sums in closed form using results from Ramanujan's theory of theta functions, continued fractions and class invariants. Many explicit examples are given.

The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion.

Van Fossen Conrad, Eric, Flajolet, Philippe (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

The generalised ellipsoidal wave equation [0,3,11].

Harold Exton (1995)

Collectanea Mathematica

Explicit solutions are obtained of the linear differential equation of the second order with three regular singularities and one irregular singularity of the first type. The behavior at the point at infinity is discussed. An important special case is an algebraic form of the ellipsoidal wave equation.

The Heun equation and the Calogero-Moser-Sutherland system. II: Perturbation and algebraic solution.

Takemura, Kouichi (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

The Legendre Formula in Clifford Analysis

Laville, Guy, Ramadanoff, Ivan (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.Let R0,2m+1 be the Clifford algebra of the antieuclidean 2m+1 dimensional space. The elliptic Cliffordian functions may be generated by the z2m+2 function, analogous to the well-known Weierstrass z-function. The latter satisfies a Legendre equality. We prove a corresponding formula at the level of the monogenic function Dm z2m+2.

The Many Limits of Mixed Means. II. The Carlson Sequences.

John Todd (1989)

Numerische Mathematik

The new properties of the theta functions

Stefan Czekalski (2013)

Annales mathématiques Blaise Pascal

It is shown, that the function $\begin{matrix} H (x) & = \sum_{k = - \infty}^{\infty} e^{- k^{2} x} \\ satisfies the relation \\ H (x) & = \sum_{n = 0}^{\infty} \frac{{(2 π)}^{2 n}}{(2 n)!} H^{(n)} (x) . \end{matrix}$

The number of representations by sums of squares and triangular numbers.

Lam, Heung Yeung (2007)

Integers

Currently displaying 1 – 20 of 39

Page 1 Next