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Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 111–123 | Cite as

Two-Sided Hypergenic Functions

  • Sirkka-Liisa Eriksson
  • Heikki Orelma
  • Nelson Vieira
Article
  • 66 Downloads

Abstract

In this paper we present an analogous of the class of two-sided axial monogenic functions to the case of axial \({\kappa}\)-hypermonogenic functions. In order to do that we will solve a Vekua-type system in terms of Bessel functions.

Keywords

Clifford algebras Hypergenic functions \({\kappa}\)-Hypergenic functions Two-side hypergenic functions 

Mathematics Subject Classification

Primary 30G20 Secondary 30G35 33C10 30A05 30B30 

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References

  1. 1.
    Brackx, F., Delanghe, R., Sommen, F.: Clifford Analysis. Pitman, Boston (1982)Google Scholar
  2. 2.
    Delanghe, R., Sommen, F., Souc̆ek, V.: Clifford Algebras and Spinor-Valued Functions. Kluwer Academic Publishers, New YorkGoogle Scholar
  3. 3.
    Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G.: Higher Transcendental Functions, vol. I, II (Bateman Manuscript Project). McGraw-Hill, New York (1953)MATHGoogle Scholar
  4. 4.
    Eriksson S.L.: Hyperbolic extensions of integral formulas. Adv. Appl. Clifford Algebra 20, 575–586 (2010)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Eriksson S.L.: Integral formulas for hypermonogenic functions. Bull. Belg. Math. Soc. 11, 705–718 (2004)MathSciNetMATHGoogle Scholar
  6. 6.
    Eriksson S.L., Leutwiler H.: Hypermonogenic functions in Clifford analysis and their applications in mathematical physics. Clifford Anal. 2, 287–302 (2000)MATHGoogle Scholar
  7. 7.
    Peña Peña D., Sommen F.: Vekua-type systems related to two-sided monogenic functions. Complex. Anal. Oper. Theory 6(2), 397–405 (2012)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Polyanin, A.D., Zaitsev, V.F.: Handbook of Exact Solutions for Ordinary Differential Equations, 2nd edn. CRC Press, Boca Raton (2003)Google Scholar
  9. 9.
    Sommen F.: Plane elliptic systems and monogenic functions in symetric domains. Red. Circ. Mat. Palermo 62(2), 259–269 (1984)MATHGoogle Scholar
  10. 10.
    Sommen F.: Special functions in Clifford analysis and axial symetry. J. Math. Anal. Appl. 130(1), 110–133 (1988)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Vekua I.N.: Analytic Functions. Pergamon Press, London (1962)MATHGoogle Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Sirkka-Liisa Eriksson
    • 1
  • Heikki Orelma
    • 1
  • Nelson Vieira
    • 2
  1. 1.Department of MathematicsTampere University of TechnologyTampereFinland
  2. 2.Department of MathematicsCIDMA, Center for Research and Development in Mathematics and ApplicationsAveiroPortugal

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