Abstract
Regular quaternionic functions inherit a version of the Cauchy Theorem from the holomorphic complex functions. Let us begin with some notations.
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References
F. Colombo, G. Gentili, I. Sabadini, A Cauchy kernel for slice regular functions. Ann. Global Anal. Geom. 37(4), 361–378 (2010)
F. Colombo, I. Sabadini, A structure formula for slice monogenic functions and some of its consequences, in Hypercomplex Analysis, ed. by I. Sabadini, M. Shapiro, F. Sommen. Trends in Mathematics (Birkhäuser, Basel, 2009), pp. 101–114
F. Colombo, I. Sabadini, D.C. Struppa, The Pompeiu formula for slice hyperholomorphic functions. Mich. Math. J. 60(1), 163–170 (2011)
J.B. Conway, Functions of one complex variable. Graduate Texts in Mathematics, vol. 11, 2nd edn. (Springer, New York, 1978)
G. Gentili, D.C. Struppa, A new theory of regular functions of a quaternionic variable. Adv. Math. 216(1), 279–301 (2007)
C. Stoppato, Regular functions of one quaternionic variable. Ph.D. thesis, advisor G. Gentili, Università degli Studi di Firenze, 2010
C. Stoppato, Singularities of slice regular functions. Math. Nachr. 285(10), 1274–1293 (2012)
F. Vlacci, The argument principle for quaternionic slice regular functions. Mich. Math. J. 60(1), 67–77 (2011)
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Gentili, G., Stoppato, C., Struppa, D.C. (2013). Integral Representations. In: Regular Functions of a Quaternionic Variable. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33871-7_6
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DOI: https://doi.org/10.1007/978-3-642-33871-7_6
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