Related papers: Formal sine functions in harmonic algebra
In this paper we define canonical sine and cosine transform, convolution operations, prove convolution theorems in space of integrable functions on real space. Further, obtain some results require to construct the spaces of integrable…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study…
We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
We give a criterion of integrality of an one-dimensional formal group law in terms of congruences satisfied by the coefficients of the canonical invariant differential. For an integral formal group law a p-adic analytic formula for the…
Many integrals in the classical table by Gradshteyn and Ryzhik can be evaluated in terms of the digamma function (= the logarithmic derivative of the gamma function). Some of them are presented here.
Based on the results of part I, we obtain the general form of the addition theorem for spin spherical harmonics and give explicit results in the cases involving one spin-$s'$ and one spin-$s$ spherical harmonics with $s',s=1/2$, 1, 3/2, and…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
Two linear recurrences exhibit mirror symmetry connecting the constants $e$ and $\pi$. When parametrized, their asymptotic connection constants extend to meromorphic functions satisfying additive functional equations with rational…
We introduce an extension of the standard cohomology which is characterised by maps that fail to be classical cocycles by products of simpler maps. The construction is motivated by the study of Manin's noncommutative modular symbols and of…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an…