129
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A generalized monogenic exponential function in ℍ

ORCID Icon
Pages 1881-1897 | Received 25 Jul 2018, Accepted 11 Dec 2018, Published online: 22 Feb 2019

References

  • Bock S, Gürlebeck K. On a generalized Appell system and monogenic power series. Math Methods Appl Sci. 2010;33:394–411.
  • Bock S. On a three dimensional analogue to the holomorphic z-powers: power series and recurrence formulae. Complex Var Elliptic Equ. 2012;57(12):1349–1370. doi: 10.1080/17476933.2010.551198
  • Bock S. On a three dimensional analogue to the holomorphic z-powers: Laurent series expansions. Complex Var Elliptic Equ. 2012;57(12):1271–1287. doi: 10.1080/17476933.2010.534792
  • Bock S. On orthogonal series expansions in dimensions 2, 3 and 4. Proceedings of the 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (ICCA9). Weimar: 2011.
  • Bock S. On a hypercomplex version of the Kelvin solution in linear elasticity. In: Drygás P, Rogosin S, editors. Modern problems in applied analysis. Basel: Birkhäuser; 2018. (Trends in mathematics).
  • Bock S. On a class of monogenic functions with (logarithmic) line singularities. Adv Appl Clifford Algebras. 2018;28:6. doi: 10.1007/s00006-018-0823-5
  • Bock S. Special classes of monogenic functions in H. Adv Appl Clifford Algebras. 2018;28:56. doi: 10.1007/s00006-018-0874-7
  • Fueter R. Analytische Funktionen einer Quaternionen-Variablen. Comm Math Helv. 1931;4:9–20. doi: 10.1007/BF01202702
  • Brackx FF. The exponential function of a quaternion variable. Appl Anal. 1979;8:265–276. doi: 10.1080/00036817908839234
  • Gürlebeck K, Habetha K, Sprößig W. Holomorphic functions in the plane and n-dimensional space. Birkhäuser; 2008.
  • Gürlebeck K, Malonek HR. A hypercomplex derivative of monogenic functions in Rn+1 and its applications. Complex Var. 1999;39:199–228.
  • Falcão MI, Cruz J, Malonek HR. Remarks on the generation of monogenic functions. Proceedings of the IKM2006. Weimar: 2006.
  • Malonek HR, Falcao MI. Generalized exponentials through Appell sets in Rn+1 and Bessel functions. AIP Conf Proc. 2007;936:738. doi: 10.1063/1.2790257
  • Gürlebeck N. On Appell sets and the Fueter-Sce mapping. Adv Appl Clifford Algebras. 2009;19:51. doi: 10.1007/s00006-008-0126-3
  • Brackx F, Delanghe R, Sommen F. Clifford analysis. London: Pitman; 1982. (Pitman research notes math. ser.; 76).
  • Bock S. On monogenic series expansions with applications to linear elasticity. Adv. Appl. Clifford Algebras. 2014;24(4):931–943. doi: 10.1007/s00006-014-0490-0
  • Malonek H. A new hypercomplex structure of the euclidean space Rm+1 and the concept of hypercomplex differentiability. Complex Var Theory Appl. 1990;14(1–4):25–33.
  • Luna-Elizarrarás ME, Shapiro M. A survey on the (hyper-) derivates in complex, quaternionic and Clifford analysis. Millan J Math. 2011;79:521–542. doi: 10.1007/s00032-011-0169-0
  • Watson GN. A treatise on the theory of Bessel functions. 2nd ed. London: Cambridge University Press; 1966. (reprint).
  • Abramowitz I, Stegun A, editors. Handbook of mathematical functions with formulas, graphs, and mathematical tables. 9th Reprinted edition. Washington (DC): National Bureau of Standards; 1964; New York: Dover Publications; 1972. (Applied mathematics series; 55).
  • Andrews LC. Special functions of mathematics for engineers. Bellingham: SPIE Optical Engineering Press; 1998.
  • Sansone G. Orthogonal functions. New York: Interscience Publishers; 1959. (Pure and applied mathematics; vol. IX).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.