On a three dimensional analogue to the holomorphicz-powers: power series and recurrence formulae

DOI10.1080/17476933.2010.551198zbMath1258.30021arXiv1007.1764OpenAlexW4229780458MaRDI QIDQ3145033

Sebastian Bock

Publication date: 13 December 2012

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.1764

zbMATH Keywords

quaternionsTaylor seriesFourier seriessolid spherical monogenicscomplete orthonormal systems

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Power series, series of functions of several complex variables (32A05) Numerical aspects of recurrence relations (65Q30)

Related Items (10)

The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces ⋮ On a class of monogenic functions with (logarithmic) line singularities ⋮ Special classes of monogenic functions in \(\mathbb {H}\) ⋮ Recent Progress on Spheroidal Monogenic Functions ⋮ Constructive Orthonormalisation of Monogenic Polynomials on a Finite Cylinder ⋮ Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains ⋮ On a Hypercomplex Version of the Kelvin Solution in Linear Elasticity ⋮ On orthogonal monogenics in oblate spheroidal domains and recurrence formulae ⋮ On monogenic series expansions with applications to linear elasticity ⋮ A generalized monogenic exponential function in ℍ

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