The Cauchy–Pompeiu integral formula in elliptic complex numbers
نویسندگان
چکیده
منابع مشابه
Elliptic complex numbers with dual multiplication
Investigated is a number system in which the square of a basis number: (w), and the square of its additive inverse: (−w), are not equal. Termed W space, a vector space over the reals, this number system will be introduced by restating defining relations for complex space C, then changing a defining conjugacy relation from conj(z) + z = 0 in the complexes to conj(z) + z = 1 for W space. This cha...
متن کاملAn Integral Duality Formula
We establish an integral formula for the duality between multilinear forms/homogeneous polynomials and tensor products for dual spaces with the approximation property and for which the injective tensor products of their preduals is separable and does not contain a copy of `1. We deduce some multilinear Bishop-Phelps-type results. Although spaces of multilinear forms and homogeneous polynomials ...
متن کاملOn the Elliptic Analogue of Jensen's Formula
Mahler's measure of a polynomial can be written as a logarithmic integral over the torus. We propose a deenition when the underlying group is an elliptic curve. Having reviewed some of the classical results in the toral case, we take some rst steps towards realising elliptic analogues. In particular, we focus on elliptic analogues of Kronecker's Theorem and Lehmer's problem. We wish to stress t...
متن کاملSchläfli numbers and reduction formula
We define so-called poset-polynomials of a graded poset and use it to give an explicit and general description of the combinatorial numbers in Schläfli’s (combinatorial) reduction formula. For simplicial and simple polytopes these combinatorial numbers can be written as functions of the numbers of faces of the polytope and the tangent numbers. We use the constructed formulas to determine the vo...
متن کاملThe Lagrange Interpolation Formula and Stirling Numbers
and the formulas may be used to extend the definition of Si(w, ¿) and S2(n, k) for arbitrary real n. In a previous paper [2] the writer has proved several apparently new formulas relating the two kinds of Stirling numbers to each other. Carlitz [l] has generalized these results in part as follows. Instead of considering the polynomial B['\ let fk(z) denote an arbitrary polynomial in z of degree...
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: Complex Variables and Elliptic Equations
سال: 2012
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476933.2010.534155