# zbMATH — the first resource for mathematics

## Ernst, Thomas

 Author ID: ernst.thomas Published as: Ernst, Thomas; Ernst, T. Homepage: http://solnaschack.org/ernst/index.html External Links: ORCID
 Documents Indexed: 47 Publications since 2001, including 2 Books Reviewing Activity: 414 Reviews

#### Co-Authors

 47 single-authored
all top 5

#### Serials

 5 Advanced Studies in Contemporary Mathematics (Kyungshang) 3 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 3 Algebras, Groups and Geometries 3 Proceedings of the Jangjeon Mathematical Society 3 Axioms 3 Special Matrices 2 Rendiconti del Seminario Matematico della Università di Padova 2 Linear Algebra and its Applications 2 Communications of the Korean Mathematical Society 2 Proceedings of the Estonian Academy of Sciences 1 Hadronic Journal 1 Demonstratio Mathematica 1 The Journal of the Indian Mathematical Society. New Series 1 Le Matematiche 1 Publications de l’Institut Mathématique. Nouvelle Série 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Czechoslovak Journal of Physics 1 Journal of Nonlinear Mathematical Physics 1 Advances in Dynamical Systems and Applications 1 International Journal of Difference Equations 1 International Journal of Combinatorics 1 Journal of Discrete Mathematics 1 Journal of Operators
all top 5

#### Fields

 35 Special functions (33-XX) 18 Combinatorics (05-XX) 9 Number theory (11-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 3 Nonassociative rings and algebras (17-XX) 3 Difference and functional equations (39-XX) 3 Operator theory (47-XX) 2 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH Open

28 Publications have been cited 177 times in 124 Documents Cited by Year
A comprehensive treatment of $$q$$-calculus. Zbl 1256.33001
Ernst, Thomas
2012
A method for $$q$$-calculus. Zbl 1041.33013
Ernst, Thomas
2003
$$q$$-Bernoulli and $$q$$-Euler polynomials, an umbral approach. Zbl 1116.39013
Ernst, Thomas
2006
The different tongues of $$q$$-calculus. Zbl 1161.33302
Ernst, Thomas
2008
Convergence aspects for $$q$$-Appell functions. I. Zbl 1294.33026
Ernst, Thomas
2014
Examples of a $$q$$-umbral calculus. Zbl 1151.33009
Ernst, Thomas
2008
An umbral approach to find $$q$$-analogues of matrix formulas. Zbl 1305.15039
Ernst, Thomas
2013
$$q$$-Leibniz functional matrices with application to $$q$$-Pascal and $$q$$-Stirling matrices. Zbl 1279.15013
Ernst, Thomas
2012
On the $$q$$-exponential of matrix $$q$$-Lie algebras. Zbl 1418.17066
Ernst, Thomas
2017
$$q$$-Pascal and $$q$$-Wronskian matrices with implications to $$q$$-Appell polynomials. Zbl 1295.05060
Ernst, Thomas
2013
Multiplication formulas for $$q$$-Appell polynomials and the multiple $$q$$-power sums. Zbl 1352.05089
Ernst, Thomas
2016
Convergence aspects for $$q$$-Lauricella functions I. Zbl 1254.33017
Ernst, Thomas
2012
$$q$$-generating functions for one and two variables. Zbl 1132.33335
Ernst, Thomas
2005
$$q$$-calculus as operational algebra. Zbl 1209.33015
Ernst, Thomas
2009
$$Q$$-deformed matrix pseudo-groups. Zbl 1195.81078
Ernst, T.
2010
The generalized Cauchy determinants. (Les déterminants généralisés de Cauchy.) Zbl 1117.15007
Ernst, Thomas
2006
Jacobi-Gudermann-Glaisher’s elliptic functions according to Heine. (Die Jacobi-Gudermann-Glaisherschen elliptischen Funktionen nach Heine.) Zbl 1226.33011
Ernst, Thomas
2010
Convergence aspects for generalizations of $$q$$-hypergeometric functions. Zbl 1318.33033
Ernst, Thomas
2015
On the symmetric $$q$$-Lauricella functions. Zbl 1347.33037
Ernst, Thomas
2016
Generalized Cauchy-Vandermonde determinants. Zbl 1082.15013
Ernst, Thomas
2005
Some results for $$q$$-functions of many variables. Zbl 1167.33308
Ernst, Thomas
2004
A renaissance for a $$q$$-umbral calculus. Zbl 1125.33014
Ernst, Thomas
2007
$$q$$-analogues of general reduction formulas by Buschman and Srivastava and an important $$q$$-operator reminding of MacRobert. Zbl 1229.33031
Ernst, Thomas
2011
On certain generalized $$q$$-Appell polynomial expansions. Zbl 1308.05021
Ernst, Thomas
2014
Factorizations of $$q$$-Pascal matrices. Zbl 1317.15012
Ernst, Thomas
2014
Expansion formulas for Apostol type $$q$$-Appell polynomials, and their special cases. Zbl 1420.11043
Ernst, Thomas
2018
Handbook for the $$q$$-analysis. (Handbuch für die $$q$$-Analysis.) Zbl 1373.33001
Ernst, Thomas
2017
On the $$q$$-analogues of Srivastava’s triple hypergeometric functions. Zbl 1301.33019
Ernst, Thomas
2013
Expansion formulas for Apostol type $$q$$-Appell polynomials, and their special cases. Zbl 1420.11043
Ernst, Thomas
2018
On the $$q$$-exponential of matrix $$q$$-Lie algebras. Zbl 1418.17066
Ernst, Thomas
2017
Handbook for the $$q$$-analysis. (Handbuch für die $$q$$-Analysis.) Zbl 1373.33001
Ernst, Thomas
2017
Multiplication formulas for $$q$$-Appell polynomials and the multiple $$q$$-power sums. Zbl 1352.05089
Ernst, Thomas
2016
On the symmetric $$q$$-Lauricella functions. Zbl 1347.33037
Ernst, Thomas
2016
Convergence aspects for generalizations of $$q$$-hypergeometric functions. Zbl 1318.33033
Ernst, Thomas
2015
Convergence aspects for $$q$$-Appell functions. I. Zbl 1294.33026
Ernst, Thomas
2014
On certain generalized $$q$$-Appell polynomial expansions. Zbl 1308.05021
Ernst, Thomas
2014
Factorizations of $$q$$-Pascal matrices. Zbl 1317.15012
Ernst, Thomas
2014
An umbral approach to find $$q$$-analogues of matrix formulas. Zbl 1305.15039
Ernst, Thomas
2013
$$q$$-Pascal and $$q$$-Wronskian matrices with implications to $$q$$-Appell polynomials. Zbl 1295.05060
Ernst, Thomas
2013
On the $$q$$-analogues of Srivastava’s triple hypergeometric functions. Zbl 1301.33019
Ernst, Thomas
2013
A comprehensive treatment of $$q$$-calculus. Zbl 1256.33001
Ernst, Thomas
2012
$$q$$-Leibniz functional matrices with application to $$q$$-Pascal and $$q$$-Stirling matrices. Zbl 1279.15013
Ernst, Thomas
2012
Convergence aspects for $$q$$-Lauricella functions I. Zbl 1254.33017
Ernst, Thomas
2012
$$q$$-analogues of general reduction formulas by Buschman and Srivastava and an important $$q$$-operator reminding of MacRobert. Zbl 1229.33031
Ernst, Thomas
2011
$$Q$$-deformed matrix pseudo-groups. Zbl 1195.81078
Ernst, T.
2010
Jacobi-Gudermann-Glaisher’s elliptic functions according to Heine. (Die Jacobi-Gudermann-Glaisherschen elliptischen Funktionen nach Heine.) Zbl 1226.33011
Ernst, Thomas
2010
$$q$$-calculus as operational algebra. Zbl 1209.33015
Ernst, Thomas
2009
The different tongues of $$q$$-calculus. Zbl 1161.33302
Ernst, Thomas
2008
Examples of a $$q$$-umbral calculus. Zbl 1151.33009
Ernst, Thomas
2008
A renaissance for a $$q$$-umbral calculus. Zbl 1125.33014
Ernst, Thomas
2007
$$q$$-Bernoulli and $$q$$-Euler polynomials, an umbral approach. Zbl 1116.39013
Ernst, Thomas
2006
The generalized Cauchy determinants. (Les déterminants généralisés de Cauchy.) Zbl 1117.15007
Ernst, Thomas
2006
$$q$$-generating functions for one and two variables. Zbl 1132.33335
Ernst, Thomas
2005
Generalized Cauchy-Vandermonde determinants. Zbl 1082.15013
Ernst, Thomas
2005
Some results for $$q$$-functions of many variables. Zbl 1167.33308
Ernst, Thomas
2004
A method for $$q$$-calculus. Zbl 1041.33013
Ernst, Thomas
2003
all top 5

#### Cited by 187 Authors

 19 Ernst, Thomas 6 Awan, Muhammad Uzair 6 Khan, Subuhi 6 Noor, Khalida Inayat 6 Noor, Muhammad Aslam 5 Kim, Taekyun 5 Riyasat, Mumtaz 4 Ahmad, Bashir 3 Araci, Serkan 3 Hounkonnou, Mahouton Norbert 3 Nahid, Tabinda 3 Neamaty, Abdolali 3 Srivastava, Hari Mohan 3 Tariboon, Jessada 3 Tourani, Mehdi 3 Wang, Guotao 2 Abdeljawad, Thabet 2 Alp, Necmettin 2 Alzabut, Jehad O. 2 Ben Geloun, Joseph 2 Bonfiglioli, Andrea 2 Budak, Hüseyin 2 Han, Zhenlai 2 Jain, Pankaj 2 Jleli, Mohamed 2 Kalsoom, Humaira 2 Katriel, Jacob 2 Kim, Dae San 2 Li, Xinhui 2 Mahmudov, Nazim Idrisoglu 2 Malinowska, Agnieszka Barbara 2 Mansour, Toufik 2 Martins, Natália F. 2 Muhyi, Abdulghani 2 Nategh, Mehdi 2 Ntouyas, Sotiris K. 2 Persson, Lars-Erik 2 Ramírez, William 2 Řehák, Pavel 2 Rim, Seog-Hoon 2 Samet, Bessem 2 Sarikaya, Mehmet Zeki 2 Schork, Matthias 2 Shaimardan, Serikbol 2 Torres, Delfim Fernando Marado 2 Urieles, Alejandro 2 Zhang, Lihong 2 Zhao, Fayou 1 Abbas, Mujahid 1 Achilles, Rüdiger 1 Acikgoz, Mehmet 1 Adwan, Eman Ahmed 1 Afif, Masmoudi 1 Agarwal, Ravi P. 1 Agheli, Bahram 1 Ahmad, Hijaz 1 Ali, Muhammad Aamir 1 Allahverdiev, Bilender Paşaoğlu 1 Alsulami, Hamed Hamdan 1 Aouf, Mohamed Kamal 1 Araújo, Amarisio S. 1 Bai, Chuanzhi 1 Băleanu, Dumitru I. 1 Basu, Chandrani 1 Batkhin, Alexandr B. 1 Bayram, Mustafa 1 Boutouria, Imen 1 Bouzida, Imed 1 Brahim, Kamel 1 Brito da Cruz, Artur M. C. 1 Budakçı, Gülter 1 Butt, Saad Ihsan 1 Cakić, Nenad P. 1 Cangul, Ismail Naci 1 Castilla, Letelier 1 Chan, O-Yeat 1 Cheon, Gi-Sang 1 Chung, Won-Sang 1 Das, Sourav 1 de Camargo, André Pierro 1 Delavar, Mohsen Rostamian 1 Dişibüyük, Çetin 1 Dolgiĭ, Dmitriĭ Viktorovich 1 Dziemiańczuk, Maciej 1 Eini Keleshteri, Marzieh 1 El-Desouky, Beih S. 1 El Moize, Othmane 1 Erden, Samet 1 Fan, Dashan 1 Fink, Thomas M. A. 1 Fitouhi, Ahmed 1 Flores-Gallegos, Nelson 1 Furtado, Helaine C. M. 1 Ghosh, Arka Prasanna 1 Gochhayat, Priyabrat 1 Goldman, Ron N. 1 Gomaa, R. S. 1 Gouvêa, Érica J. C. 1 Guo, Jiuhua 1 Hobiny, Aatef D. ...and 87 more Authors
all top 5

#### Cited in 75 Serials

 6 Applied Mathematics and Computation 6 Linear Algebra and its Applications 6 Axioms 5 Abstract and Applied Analysis 5 Advances in Difference Equations 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Special Matrices 3 Journal of Function Spaces 2 Journal of Mathematical Physics 2 Reports on Mathematical Physics 2 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 2 Czechoslovak Mathematical Journal 2 Demonstratio Mathematica 2 Journal of Computational and Applied Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Applied Mathematics Letters 2 The Ramanujan Journal 2 Journal of Inequalities and Applications 2 Communications of the Korean Mathematical Society 2 Tbilisi Mathematical Journal 2 Afrika Matematika 2 Arabian Journal of Mathematics 2 Journal of Mathematics 2 Korean Journal of Mathematics 1 Advances in Applied Probability 1 Computers & Mathematics with Applications 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 Fortschritte der Physik 1 Journal of Algebra 1 Journal of the Korean Mathematical Society 1 Journal of Pure and Applied Algebra 1 Le Matematiche 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerical Functional Analysis and Optimization 1 Programming and Computer Software 1 Quaestiones Mathematicae 1 Bulletin of the Korean Mathematical Society 1 Bulletin of the Iranian Mathematical Society 1 Optimization 1 Forum Mathematicum 1 European Journal of Operational Research 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Combinatorics 1 Russian Journal of Mathematical Physics 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Turkish Journal of Mathematics 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Journal of Mathematical Chemistry 1 Discrete Dynamics in Nature and Society 1 Methodology and Computing in Applied Probability 1 Mathematical Modelling and Analysis 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Journal of the Australian Mathematical Society 1 Applied Mathematics E-Notes 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Journal of Applied Mathematics and Computing 1 Mediterranean Journal of Mathematics 1 Complex Analysis and Operator Theory 1 Frontiers of Mathematics in China 1 Journal of Mathematical Inequalities 1 Electronic Research Announcements in Mathematical Sciences 1 Advances in Mathematical Physics 1 International Journal of Combinatorics 1 Journal of Pseudo-Differential Operators and Applications 1 Symmetry 1 Eurasian Mathematical Journal 1 Analysis and Mathematical Physics 1 Mathematics 1 Journal of Discrete Mathematics 1 Journal of Operators 1 Cogent Mathematics 1 Journal of Siberian Federal University. Mathematics & Physics
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#### Cited in 34 Fields

 43 Special functions (33-XX) 32 Combinatorics (05-XX) 29 Number theory (11-XX) 28 Difference and functional equations (39-XX) 23 Real functions (26-XX) 10 Ordinary differential equations (34-XX) 8 Quantum theory (81-XX) 7 Nonassociative rings and algebras (17-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Probability theory and stochastic processes (60-XX) 5 Numerical analysis (65-XX) 4 Operations research, mathematical programming (90-XX) 3 Operator theory (47-XX) 2 Commutative algebra (13-XX) 2 Associative rings and algebras (16-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)