Thomas Ernst

I am a Ph.D. in mathematics (Uppsala 2002) and a Master of Science in Engineering Physics from Lund at the Department of Mathematics of Uppsala University.

I am interested in q-calculus, complex analysis, algebra and physics.

Publications:

• A new method for q-hypergeometric series. Czech. J. of Physics 51, 2001, No. 12
• A new method for q-calculus. Uppsala Dissertations in Mathematics 25, 2002.
• A method for q-calculus. J. nonlinear Math. Physics, No.10, 2003, 487--525.
• Some results for q-functions of many variables. Rendiconti di Padova 112, 2004, 199--235.
• Generalized Cauchy-Vandermonde determinants. Advan. Stud. Contemp. Math. 11 no. 1, 2005, 1--10.
• q-Generating funtions for one and two variables. Simon Stevin 12 no. 4, 2005, 589--605.
• q-Bernoulli and q-Euler Polynomials, An Umbral Approach. International journal of difference equations 1 no. 1, 2006, 31--80.
• Les déterminants généralisés de Cauchy. Advances in Dynamical Systems and Applications 1 no. 1, 2006, 59--77.
• q-analogues of some operational formulas. Algebras Groups Geom. 23 no. 4, 2006, 354--374.
• Some new formulas involving Γ_q functions. Rendiconti di Padova, 118, 2007, 159--188
• Examples of a q-umbral calculus. Advan. Stud. Contemp. Math, {16}(1), 2008, 1--22
• Motivation for Introducing q-Complex Numbers. ADSA Special Volume in Honor of Allan Peterson, 3(1), 2008, 107--129
• q-Stirling numbers, an umbral approach. Advances in Dynamical Systems and Applications, 3(2), 2008, 251--282
• The different tongues of q-calculus, Proceedings of Estonian Academy of Sciences, {57} no.2, 2008, 81--99
• q-calculus as operational algebra. Proceedings of Estonian Academy of Sciences, no 58(2), 2009, 73--97
• q-deformed matrix pseudo--groups. Royal Flemish Academy of Belgium, 2010
• Sur les polynômes q-Hermite de Cigler. Algebras Groups Geom. 27, 121-142 2010 (French)
• Die Jacobi--Gudermann--Glaisher elliptischen Funktionen nach Heine. Hadronic J. no 33, 273-302 2010.
• Zur Theorie der Γ_q-Funktion Proceedings Jangjeon Math. Soc. 14 2011, 91-113
• q-analogues of general reduction formulas by Buschman and Srivastava and an important q-operator reminding of MacRobert. Demonstratio Mathematica No. 2 Vol.44 2011, 285-296
• On certain generalizations of q-hypergeometric functions of two variable. International Journal of Mathematics and computation 16 2012, 1-27.
• q-analogues of triple series reduction formulas due to Srivastava and Panda with general terms. ADSA 7, No 1 (2012), 41-55.
• Convergence aspects for q-Lauricella functions 1. Adv. Studies Contemp. Math. 22 (1), 2012
• A comprehensive treatment of q-calculus, Birkhäuser 2012
• q-Leibniz functional matrices with applications to q-Pascal and q-Stirling matrices. Adv. Studies Contemp. Math 22(4), 2012
• On the character of q-quadratic transformations. IJDE 7(2) 2012, 139-150.
• q-Pascal and q-Wronskian matrices with implications to q-Appell polynomials. J.discrete math. 2013
• q-functions of many variables in the spirit of Whipple and Srivastava. Proc. Jangjeon Math. Soc. 16(1) 2013
• Multiple q-hypergeometric transformations involving q-integrals. Proceedings of the 9th Annual Conference of the Society for Special Functions and their Applications (SSFA) 2010 9, 91-99
• On the q-analogues of Srivastava's triple hypergeometric functions. Axioms 2(2), 85-99: 2013
• An umbral approach to find q-analogues of matrix formulas. Linear Algebra and its Applications. 439(2013),no. 4, 1167-1182
• Convergence aspects for q-Appell functions I. J. Indian math. soc. 81 no. 1-2 (2014), 67-77
• Decomposition formulas for triple q-hypergeometric functions. Int. J. Comb. 2014, Article ID 712321, 14 p. (2014).
• Faktorisierungen von q-Pascalmatrizen. Algebras Groups Geom. 31, No. 4, 387-405 (2014).
• On ordinary, linear q-difference equations, with applications to q-Sato theory J. Oper. 2015, Art. ID 824549, 8 pp.
• A solid Foundation for q-Appell Polynomials. ADSA 10 2015, 27-35
• On certain generalized q-Appell polynomial expansions. Ann. Univ. Marie Curie, Sect. A 68,- No. 2, 27-50 (2015).
• Convergence Aspects for Generalizations of q-Hypergeometric Functions. Axioms 2015
• On elliptic and hyperbolic modular functions and the corresponding Gudermann Peeta functions. Axioms 2015
• Factorizations for q-Pascal matrices of two variables. Spec. Matrices 3, 207-213 (2015)
• On the symmetric q-Lauricella functions. Proc. Jangjeon Math. Soc. 19, No. 2, 319-344 (2016)
• Zur Theorie der Γ_q-Funktion und der Ψ_q-Funktion. Adv. Stud. Contemp. Math., Kyungshang 26, No. 2, 307-321 (2016)
• Multiplication formulas for q-Appell polynomials and the multiple q-power sums. Ann. Univ. Mariae Curie-Sk lodowska Sect. A 70 1, 1-18. 2016
• On the q-exponential of matrix q-Lie algebras. Spec. Matrices 5, 36-50 2017
• Handbuch für die q-Analysis. Logos Verlag, Berlin 2017
• Expansion formulas for Apostol type q-Appell polynomials, and their special cases. Accepted in Le Matematiche.
• On several q-special matrices,including the q-Bernoulli and q-Euler matrices. Accepted in Linear Algebra and its Applications
• On Eulerian q-integrals for single and multiple q-hypergeometric series. Accepted in Communications of the Korean Mathematical Society

Reports:

• A new q-Taylor formula. U.U.D.M. Report 1999:4, 10 pp.
• (with Silvestrov, S. D.) Shift difference equations, symmetric polynomials and representations of the symmetric group. U. U. D. M. Report 1999:14.
• A new notation for q-calculus and a new q-Taylor formula. U. U. D. M. Report 1999:25.
• Generalized Vandermonde determinants. U. U. D. M. Report 2000:6.
• A new Vandermonde-related determinant and its connection to difference equations. U. U. D. M. Report 2000:9.
• The History of q-Calculus and a new Method (Licentiate Thesis). U. U. D. M. Report 2000:16.
• A New Method and its Application to Generalized q-Bessel Polynomials. U. U. D. M. Report 2001:10.
• Some results for q-Laguerre polynomials. U. U. D. M. Report 2002:20.
• q-Generating funtions for one and two variables. U. U. D. M. Report 2002:21.
• Some results for q-functions of many variables U.U.D.M. Report 2004:3
• q-Analogues of some operational formulas U.U.D.M. Report 2004:4
• q-Bernoulli and q-Stirling numbers, an umbral approach, U. U. D. M. Report 2005:46
• Some new formulas involving Γ_q functions. U. U. D. M. Report 2006:34
• Some results for q -functions of many variables II U. U. D. M. Report 2007:43
• q-complex numbers, a natural consequence of umbral calculus U. U. D. M. Report 2007:44
• Die Jacobi--Gudermann--Glaisher elliptischen Funktionen nach Heine U. U. D. M. Report 2007:45
• q-Pascal and q-Bernoulli matrices, an umbral approach, U. U. D. M. Report 2008:23
• Examples of q-orthogonal polynomials, U. U. D. M. Report 2008:24
• q-deformed matrix pseudo--groups, U. U. D. M. Report 2009:16
• q-Bernoulli and q-Euler polynomials, an umbral approach II, U. U. D. M. Report 2009:17
• On the theory of the Γ_q function, U. U. D. M. Report 2009:18
• q-Taylor formulas with q-integral remainder, U. U. D. M. Report 2009:19
• Some results for q-functions of many variables III, U. U. D. M. Report 2010:10
• Convergence aspects for q--Appell functions I, U. U. D. M. Report 2010:11

CV:

• In English
• In Swedish

Research information:

• Forskningsbeskrivning (Swedish)
• Projekt-/Forskningsbeskrivning (Swedish)
• Plan for the scientific work (Swedish)
• Development of q-calculus for studies of many-particle quantum systems
• Convergence aspects for q--Appell functions II
• On q-real numbers

Links:

• q-series conference 2000
• conference progress on difference equations 2007
• Member of research group on Complex geometry and analysis
• En vacker bro mellan matematik och fysik.(In Swedish)
• Mathematics Genealogy Project
• OeMG+DMV Kongress Graz 2009
• Analysis and Applied Mathematics (ICNAAM 2010)
• Noncommutative Structures in Mathematics and PhysicsBrussels, July 22-26, 2008
• Special Functions and Orthogonal Polynomialsof Lie Groups and their Applications Decín, August 14-20, 2011
• ILAS Conference Pure and Applied Linear Algebra: The new Generation August 22-26, 2011
• Conference on "Moduli Operads and Dynamics", at Buskerud University College. July 9-12, 2103 Kongsberg
• European Wolfram Technology Conference Frankfurt, 11-12 June 2013
• 18th International Congress of the ÖMG Innsbruck, September 23-27, 2013
• Group 30, Gent July 14-- 18 2014
• 20th Conference of the International Linear Algebra Society (ILAS) July 11-15 2016
• 7th European Congress of Mathematics, July 18 - 22, 2016
• ÖMG-DMV-Congress 2017 - Universität Salzburg
• Link from Zentralblatt math

How to reach me:

• Room 14205, Angstrom laboratory, Uppsala
• 018-261924
• Department of Mathematics, Uppsala universitet, Box 480, SE-751 06 Uppsala

---

Thomas Ernst
thomas@math.uu.se, 2015-05-20