Edit Profile (opens in new tab) Ernst, Thomas Compute Distance To: Compute Author ID: ernst.thomas Published as: Ernst, Thomas; Ernst, T. Homepage: http://solnaschack.org/ernst/index.html External Links: ORCID Documents Indexed: 51 Publications since 2001, including 2 Books Reviewing Activity: 448 Reviews Co-Authors: 1 Co-Author with 1 Joint Publication 5 Co-Co-Authors Co-Authors 50 single-authored 1 Karlsson, Per W. all top 5 Serials 5 Advanced Studies in Contemporary Mathematics (Kyungshang) 4 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 4 Special Matrices 3 Algebras, Groups and Geometries 3 Proceedings of the Jangjeon Mathematical Society 3 Axioms 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 Acta et Commentationes Universitatis Tartuensis de Mathematica 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 1 Applied Analysis and Optimization all top 5 Fields 38 Special functions (33-XX) 20 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) 2 History and biography (01-XX) 2 Topological groups, Lie groups (22-XX) 2 Operator theory (47-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 33 Publications have been cited 249 times in 182 Documents Cited by ▼ Year ▼ A comprehensive treatment of \(q\)-calculus. Zbl 1256.33001Ernst, Thomas 127 2012 A method for \(q\)-calculus. Zbl 1041.33013Ernst, Thomas 32 2003 \(q\)-Bernoulli and \(q\)-Euler polynomials, an umbral approach. Zbl 1116.39013Ernst, Thomas 15 2006 The different tongues of \(q\)-calculus. Zbl 1161.33302Ernst, Thomas 9 2008 Examples of a \(q\)-umbral calculus. Zbl 1151.33009Ernst, Thomas 7 2008 Convergence aspects for \(q\)-Appell functions. I. Zbl 1294.33026Ernst, Thomas 6 2014 An umbral approach to find \(q\)-analogues of matrix formulas. Zbl 1305.15039Ernst, Thomas 6 2013 On the \(q\)-exponential of matrix \(q\)-Lie algebras. Zbl 1418.17066Ernst, Thomas 5 2017 Multiplication formulas for \(q\)-Appell polynomials and the multiple \(q\)-power sums. Zbl 1352.05089Ernst, Thomas 4 2016 \(q\)-Leibniz functional matrices with application to \(q\)-Pascal and \(q\)-Stirling matrices. Zbl 1279.15013Ernst, Thomas 4 2012 Convergence aspects for \(q\)-Lauricella functions I. Zbl 1254.33017Ernst, Thomas 4 2012 \(q\)-Pascal and \(q\)-Wronskian matrices with implications to \(q\)-Appell polynomials. Zbl 1295.05060Ernst, Thomas 3 2013 \(Q\)-deformed matrix pseudo-groups. Zbl 1195.81078Ernst, T. 3 2010 \(q\)-generating functions for one and two variables. Zbl 1132.33335Ernst, Thomas 2 2005 The generalized Cauchy determinants. (Les déterminants généralisés de Cauchy.) Zbl 1117.15007Ernst, Thomas 2 2006 Expansion formulas for Apostol type \(q\)-Appell polynomials, and their special cases. Zbl 1420.11043Ernst, Thomas 2 2018 \(q\)-calculus as operational algebra. Zbl 1209.33015Ernst, Thomas 2 2009 \(q\)-analogues of general reduction formulas by Buschman and Srivastava and an important \(q\)-operator reminding of MacRobert. Zbl 1229.33031Ernst, Thomas 1 2011 Jacobi-Gudermann-Glaisher’s elliptic functions according to Heine. (Die Jacobi-Gudermann-Glaisherschen elliptischen Funktionen nach Heine.) Zbl 1226.33011Ernst, Thomas 1 2010 A renaissance for a \(q\)-umbral calculus. Zbl 1125.33014Ernst, Thomas 1 2007 Generalized Cauchy-Vandermonde determinants. Zbl 1082.15013Ernst, Thomas 1 2005 On certain generalized \(q\)-Appell polynomial expansions. Zbl 1308.05021Ernst, Thomas 1 2014 Factorizations of \(q\)-Pascal matrices. Zbl 1317.15012Ernst, Thomas 1 2014 Convergence aspects for generalizations of \(q\)-hypergeometric functions. Zbl 1318.33033Ernst, Thomas 1 2015 Some results for \(q\)-functions of many variables. Zbl 1167.33308Ernst, Thomas 1 2004 On the exponential and trigonometric \(q,\omega \)-special functions. Zbl 1480.33006Ernst, Thomas 1 2020 On the complex \(q\)-Appell polynomials. Zbl 1473.11050Ernst, Thomas 1 2020 On Eulerian \(q\)-integrals for single and multiple \(q\)-hypergeometric series. Zbl 1396.33029Ernst, Thomas 1 2018 On several \(q\)-special matrices, including the \(q\)-Bernoulli and \(q\)-Euler matrices. Zbl 1431.11034Ernst, Thomas 1 2018 On the \(q\)-analogues of Srivastava’s triple hypergeometric functions. Zbl 1301.33019Ernst, Thomas 1 2013 Handbook for the \(q\)-analysis. (Handbuch für die \(q\)-Analysis.) Zbl 1373.33001Ernst, Thomas 1 2017 On the symmetric \(q\)-Lauricella functions. Zbl 1347.33037Ernst, Thomas 1 2016 On the \(q\)-Lie group of \(q\)-Appell polynomial matrices and related factorizations. Zbl 1430.11029Ernst, Thomas 1 2018 On the exponential and trigonometric \(q,\omega \)-special functions. Zbl 1480.33006Ernst, Thomas 1 2020 On the complex \(q\)-Appell polynomials. Zbl 1473.11050Ernst, Thomas 1 2020 Expansion formulas for Apostol type \(q\)-Appell polynomials, and their special cases. Zbl 1420.11043Ernst, Thomas 2 2018 On Eulerian \(q\)-integrals for single and multiple \(q\)-hypergeometric series. Zbl 1396.33029Ernst, Thomas 1 2018 On several \(q\)-special matrices, including the \(q\)-Bernoulli and \(q\)-Euler matrices. Zbl 1431.11034Ernst, Thomas 1 2018 On the \(q\)-Lie group of \(q\)-Appell polynomial matrices and related factorizations. Zbl 1430.11029Ernst, Thomas 1 2018 On the \(q\)-exponential of matrix \(q\)-Lie algebras. Zbl 1418.17066Ernst, Thomas 5 2017 Handbook for the \(q\)-analysis. (Handbuch für die \(q\)-Analysis.) Zbl 1373.33001Ernst, Thomas 1 2017 Multiplication formulas for \(q\)-Appell polynomials and the multiple \(q\)-power sums. Zbl 1352.05089Ernst, Thomas 4 2016 On the symmetric \(q\)-Lauricella functions. Zbl 1347.33037Ernst, Thomas 1 2016 Convergence aspects for generalizations of \(q\)-hypergeometric functions. Zbl 1318.33033Ernst, Thomas 1 2015 Convergence aspects for \(q\)-Appell functions. I. Zbl 1294.33026Ernst, Thomas 6 2014 On certain generalized \(q\)-Appell polynomial expansions. Zbl 1308.05021Ernst, Thomas 1 2014 Factorizations of \(q\)-Pascal matrices. Zbl 1317.15012Ernst, Thomas 1 2014 An umbral approach to find \(q\)-analogues of matrix formulas. Zbl 1305.15039Ernst, Thomas 6 2013 \(q\)-Pascal and \(q\)-Wronskian matrices with implications to \(q\)-Appell polynomials. Zbl 1295.05060Ernst, Thomas 3 2013 On the \(q\)-analogues of Srivastava’s triple hypergeometric functions. Zbl 1301.33019Ernst, Thomas 1 2013 A comprehensive treatment of \(q\)-calculus. Zbl 1256.33001Ernst, Thomas 127 2012 \(q\)-Leibniz functional matrices with application to \(q\)-Pascal and \(q\)-Stirling matrices. Zbl 1279.15013Ernst, Thomas 4 2012 Convergence aspects for \(q\)-Lauricella functions I. Zbl 1254.33017Ernst, Thomas 4 2012 \(q\)-analogues of general reduction formulas by Buschman and Srivastava and an important \(q\)-operator reminding of MacRobert. Zbl 1229.33031Ernst, Thomas 1 2011 \(Q\)-deformed matrix pseudo-groups. Zbl 1195.81078Ernst, T. 3 2010 Jacobi-Gudermann-Glaisher’s elliptic functions according to Heine. (Die Jacobi-Gudermann-Glaisherschen elliptischen Funktionen nach Heine.) Zbl 1226.33011Ernst, Thomas 1 2010 \(q\)-calculus as operational algebra. Zbl 1209.33015Ernst, Thomas 2 2009 The different tongues of \(q\)-calculus. Zbl 1161.33302Ernst, Thomas 9 2008 Examples of a \(q\)-umbral calculus. Zbl 1151.33009Ernst, Thomas 7 2008 A renaissance for a \(q\)-umbral calculus. Zbl 1125.33014Ernst, Thomas 1 2007 \(q\)-Bernoulli and \(q\)-Euler polynomials, an umbral approach. Zbl 1116.39013Ernst, Thomas 15 2006 The generalized Cauchy determinants. (Les déterminants généralisés de Cauchy.) Zbl 1117.15007Ernst, Thomas 2 2006 \(q\)-generating functions for one and two variables. Zbl 1132.33335Ernst, Thomas 2 2005 Generalized Cauchy-Vandermonde determinants. Zbl 1082.15013Ernst, Thomas 1 2005 Some results for \(q\)-functions of many variables. Zbl 1167.33308Ernst, Thomas 1 2004 A method for \(q\)-calculus. Zbl 1041.33013Ernst, Thomas 32 2003 all cited Publications top 5 cited Publications all top 5 Cited by 279 Authors 21 Ernst, Thomas 14 Budak, Hüseyin 13 Ali, Muhammad Aamir 9 Chu, Yuming 7 Awan, Muhammad Uzair 7 Noor, Muhammad Aslam 6 Khan, Subuhi 6 Kim, Taekyun 6 Noor, Khalida Inayat 6 Tariboon, Jessada 5 Alp, Necmettin 5 Riyasat, Mumtaz 4 Abbas, Mujahid 4 Ahmad, Bashir 4 Jain, Pankaj 4 Kalsoom, Humaira 4 Nonlaopon, Kamsing 4 Samei, Mohammad Esmael 4 Sarikaya, Mehmet Zeki 4 Sun, Shurong 3 Abdeljawad, Thabet 3 Alzabut, Jehad O. 3 Araci, Serkan 3 Basu, Chandrani 3 Han, Zhenlai 3 Hounkonnou, Mahouton Norbert 3 Kim, Dae San 3 Mishra, Shashi Kant 3 Nahid, Tabinda 3 Neamaty, Abdolali 3 Ntouyas, Sortiris K. 3 Ntouyas, Sotiris K. 3 Panda, Geetanjali 3 Panwar, Vivek 3 Qin, Zhongyun 3 Ram, Bhagwat 3 Rezapour, Shahram 3 Samet, Bessem 3 Srivastava, Hari Mohan 3 Tourani, Mehdi 3 Wang, Guotao 3 You, Xuexiao 2 Agarwal, Praveen 2 Akkurt, Abdullah 2 Bai, Chuanzhi 2 Băleanu, Dumitru I. 2 Ben Geloun, Joseph 2 Benchohra, Mouffak 2 Bonfiglioli, Andrea 2 Chakraborty, Suvra Kanti 2 Erden, Samet 2 Flores-Gallegos, Nelson 2 İşcan, İmdat 2 Jleli, Mohamed Boussairi 2 Kashuri, Artion 2 Katriel, Jacob 2 Kunt, Mehmet 2 Latif, Muhammad Amer 2 Li, Xinhui 2 Mahmudov, Nazim Idrisoglu 2 Malinowska, Agnieszka Barbara 2 Mansour, Toufik 2 Martins, Natália F. 2 Muhyi, Abdulghani 2 Murtaza, Ghulam 2 Nategh, Mehdi 2 Persson, Lars-Erik 2 Purohit, Sunil Dutt 2 Ramírez, William 2 Řehák, Pavel 2 Rim, Seog-Hoon 2 Schork, Matthias 2 Selvakumaran, Kuppathai A. 2 Shaimardan, Serikbol 2 Sitthiwirattham, Thanin 2 Thongjob, Suriyakamol 2 Torres, Delfim Fernando Marado 2 Urieles, Alejandro 2 Yasmin, Ghazala 2 Zhang, Lihong 2 Zhao, Fayou 1 Abbas, Said 1 Abdullah Alderremy, Aisha 1 Achilles, Rüdiger 1 Acikgoz, Mehmet 1 Adwan, Eman Ahmed 1 Afif, Masmoudi 1 Agarwal, Ravi P. 1 Agheli, Bahram 1 Aglić Aljinović, Andrea 1 Ahmad, Hijaz 1 Ahmadian, Ali 1 Allahverdiev, Bilender Paşaoğlu 1 Allahviranloo, Tofigh 1 Alqudah, Manar A. 1 Al-saedi, Ahmed Eid Salem 1 Alsulami, Hamed Hamdan 1 Aly, Shaban A. H. 1 Ansary, Md Abu Talhamainuddin 1 Anwar, Matloob ...and 179 more Authors all top 5 Cited in 90 Serials 20 Advances in Difference Equations 7 Applied Mathematics and Computation 7 AIMS Mathematics 6 Linear Algebra and its Applications 6 Axioms 5 Abstract and Applied Analysis 5 Journal of Inequalities and Applications 5 Journal of Applied Mathematics and Computing 5 Open Mathematics 4 Special Matrices 4 Journal of Function Spaces 3 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Journal of Mathematical Physics 2 Reports on Mathematical Physics 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 Indagationes Mathematicae. New Series 2 Journal of Mathematical Sciences (New York) 2 Computational and Applied Mathematics 2 Turkish Journal of Mathematics 2 Journal of Mathematical Chemistry 2 The Ramanujan Journal 2 Discrete Dynamics in Nature and Society 2 Communications of the Korean Mathematical Society 2 Acta Mathematica Scientia. Series B. (English Edition) 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 Nuclear Physics. B 1 Ukrainian Mathematical Journal 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 Mathematica Slovaca 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 Acta Mathematica Hungarica 1 Bulletin of the Iranian Mathematical Society 1 Optimization 1 Journal of Symbolic Computation 1 Forum Mathematicum 1 European Journal of Operational Research 1 Journal of Algebraic Combinatorics 1 The Journal of Analysis 1 Russian Journal of Mathematical Physics 1 Fractals 1 Journal of Difference Equations and Applications 1 Boletín de la Sociedad Matemática Mexicana. Third Series 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 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Mediterranean Journal of Mathematics 1 Proyecciones 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 Asian-European Journal of Mathematics 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 Azerbaijan Journal of Mathematics 1 Analysis and Mathematical Physics 1 Mathematics 1 Journal of Discrete Mathematics 1 Journal of Operators 1 International Journal of Applied and Computational Mathematics 1 Cogent Mathematics 1 Journal of Siberian Federal University. Mathematics & Physics 1 Mathematical Foundations of Computing all top 5 Cited in 36 Fields 59 Real functions (26-XX) 57 Combinatorics (05-XX) 51 Special functions (33-XX) 42 Difference and functional equations (39-XX) 34 Number theory (11-XX) 17 Ordinary differential equations (34-XX) 10 Quantum theory (81-XX) 8 Numerical analysis (65-XX) 7 Nonassociative rings and algebras (17-XX) 7 Operations research, mathematical programming (90-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Probability theory and stochastic processes (60-XX) 4 Functions of a complex variable (30-XX) 3 Partial differential equations (35-XX) 3 Integral transforms, operational calculus (44-XX) 3 Computer science (68-XX) 3 Information and communication theory, circuits (94-XX) 2 Commutative algebra (13-XX) 2 Associative rings and algebras (16-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX) Citations by Year