Edit Profile (opens in new tab) Thomae, Carl Johannes (b. 1840 d. 1921) Author ID: thomae.johannes Published as: Thomae, J.; Thomae, Joh. External Links: MacTutor · MGP · Wikidata · GND · IdRef Documents Indexed: 116 Publications since 1866, including 8 Books Biographic References: 2 Publications Co-Authors 116 single-authored all top 5 Serials 28 (Schlömilch’s) Zeitschrift für Mathematik und Physik 10 Journal für die Reine und Angewandte Mathematik 6 Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen 4 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 3 Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse 2 Mathematische Annalen 2 Annali di Matematica Pura ed Applicata. II. Serie 1 Historisch-litterarische Abteilung von (Schlömilch’s) Zeitschrift für Mathematik und Physik all top 5 Fields 15 Special functions (33-XX) 13 Algebraic geometry (14-XX) 9 Functions of a complex variable (30-XX) 6 Real functions (26-XX) 6 Ordinary differential equations (34-XX) 3 Difference and functional equations (39-XX) 3 Sequences, series, summability (40-XX) 3 Geometry (51-XX) 2 Number theory (11-XX) 2 General topology (54-XX) 2 Manifolds and cell complexes (57-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 21 Publications have been cited 133 times in 120 Documents Cited by ▼ Year ▼ Contributions to the theory of functions representable by Heine’s series \[ 1+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{b}}{1-q^{c}}x+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{a+1}}{1 q}\cdot\frac{1-q^{b}}{1-q^{c}}\cdot\frac{1-q^{b+1}}{1-q^{c+1}}x^{2}+\ldots \]. (Beiträge zur Theorie der durch die Heine’sche Reihe \[ 1+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{b}}{1-q^{c}}x+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{a+1}}{1-q}\cdot\frac{1-q^{b}}{1-q^{c}}\cdot\frac{1-q^{b+1}}{1-q^{c+1}}x^{2}+\ldots \] darstellbaren Functionen.) JFM 02.0122.04Thomae, J. 47 1869 Contribution to the determination of \(\vartheta(0,0,\ldots,0)\) by the class modules of algebraic functions. (Beitrag zur Bestimmung von \(\vartheta (0, 0,\dots 0)\) durch die Klassenmoduln algebraischer Funktionen.) JFM 02.0244.01Thomae, J. 22 1870 On the Functions which are represented by series of the form: \[ 1+\frac p1\;\frac {p'}{q'}\;\frac {p''}{q''} +\frac p1\;\frac {p+1}2\;\frac {p'}{q'}\;\frac {p'+1}{q'+1}\;\frac {p''}{q''}\;\frac {p''+1}{q''+1} +\dotsm . \]. (Ueber die Functionen, welche durch Reihen von der Form dargestellt werden: \[ 1+\frac p1\;\frac {p'}{q'}\;\frac {p''}{q''} +\frac p1\;\frac {p+1}2\; \frac {p'}{q'}\;\frac {p'+1}{q'+1}\;\frac {p''}{q''}\;\frac {p''+1}{q''+1} +\dotsm . \].) JFM 11.0336.02Thomae, J. 14 1879 On the higher hypergeometric series, in particular on the series: \[ 1+\frac{a_{0}a_{1}a_{2}}{1\cdot b_{1}b_{2}}x+\frac{a_{0}(a_{0}+1)a_{1}(a_{1}+1)a_{2}(a_{2}+1)}{1\cdot 2\cdot b_{1}(b_{1}+1)b_{2}(b_{2}+1)}\;x^{2}+\cdots\,. \]. (Ueber die höheren hypergeometrischen Reihen, insbesondere über die Reihe: \[ 1+\frac{a_{0}a_{1}a_{2}}{1\cdot b_{1}b_{2}}x+\frac{a_{0}(a_{0}+1)a_{1}(a_{1}+1)a_{2}(a_{2}+1)}{1\cdot 2\cdot b_{1}(b_{1}+1)b_{2}(b_{2}+1)}\;x^{2}+\cdots\,. \].) JFM 02.0122.01Thomae, J. 12 1870 Outline of a theory of complex functions and of theta functions of one variable. (Abriss einer Theorie der complexen Functionen und der Thetafunctionen einer Veränderlichen.) JFM 05.0218.01Thomae, J. 8 1873 The higher Heine series, or series \(F(a,a',..a^{(h)},b',..b^{(h)},q,x)\). (Les séries Heinéennes supérieures, ou les séries \(F(a, a', ..a^{(h)}, b', .. b^{(h)}, q, x)\).) JFM 03.0108.01Thomae, J. 7 1870 Bestimmung von \(d\lg\vartheta(0,0,\ldots 0)\) durch die Classenmoduln. ERAM 066.1717cjThomae, J. 4 1866 Elementary theory of analytic functions of a complex variable. (Elementare Theorie der analytischen Functionen einer complexen Veränderlichen.) JFM 12.0306.01Thomae, J. 3 1880 Elementary Theory of Analytic Functions of a Complex Variable. Second Edition. (Elementare Theorie der analytischen Functionen einer complexen Veränderlichen. 2. Aufl.) JFM 29.0334.01Thomae, J. 2 1898 Ueber die Differentiirbarkeit eines Integrales nach der oberen Grenze. JFM 25.0478.01Thomae, J. 2 1893 Theorems from the theory of functions. (Sätze aus der Functionentheorie.) JFM 10.0278.01Thomae, J. 2 1878 Dreieck aus den Mittelloten der Seiten bis zum Umkreismittelpunkt zu konstruieren. JFM 44.0597.01Thomae, J. 1 1913 Gedankenlose Denker. Eine Ferienplauderei. JFM 37.0062.04Thomae, J. 1 1906 Projektiver Beweis einiger elementaren Sätze aus der Theorie der ebenen Kurven dritter Ordnung. JFM 33.0566.01Thomae, J. 1 1902 Ueber den Zusammenhang zwischen den Steiner’schen und den Poncelet’schen Polygonen. JFM 26.0620.01Thomae, J. 1 1895 Die Kegelschnitte in rein projectiver Behandlung. JFM 25.0986.04Thomae, Joh. 1 1894 Integration by parts. (Die partielle Integration.) JFM 07.0145.02Thomae, J. 1 1875 Introduction to the theory of definite integrals. Halle, Nebert. Recension by P. du Bois Raymond. (Einleitung in die Theorie der bestimmten Integrale. Halle, Nebert. Recension von P. du Bois-Raymond.) JFM 07.0153.01Thomae, J. 1 1875 On the limits of convergence and divergence of infinite series with positive terms. (Sur les limites de la convergence et de la divergence des séries infinies à termes positifs.) JFM 04.0100.01Thomae, J. 1 1871 Sketch of a Theory of complex functions and of theta functions of one variable. (Abriss einer Theorie der complexen Funktionen und der Thetafunktionen einer Veränderlichen.) JFM 02.0187.01Thomae, J. 1 1870 Outline of a theory of complex functions and of the theta functions of one variable. (Abriss einer Theorie der complexen Funktionen und der Thetafunktionen einer Veränderlichen.) JFM 02.0220.02Thomae, J. 1 1870 Dreieck aus den Mittelloten der Seiten bis zum Umkreismittelpunkt zu konstruieren. JFM 44.0597.01Thomae, J. 1 1913 Gedankenlose Denker. Eine Ferienplauderei. JFM 37.0062.04Thomae, J. 1 1906 Projektiver Beweis einiger elementaren Sätze aus der Theorie der ebenen Kurven dritter Ordnung. JFM 33.0566.01Thomae, J. 1 1902 Elementary Theory of Analytic Functions of a Complex Variable. Second Edition. (Elementare Theorie der analytischen Functionen einer complexen Veränderlichen. 2. Aufl.) JFM 29.0334.01Thomae, J. 2 1898 Ueber den Zusammenhang zwischen den Steiner’schen und den Poncelet’schen Polygonen. JFM 26.0620.01Thomae, J. 1 1895 Die Kegelschnitte in rein projectiver Behandlung. JFM 25.0986.04Thomae, Joh. 1 1894 Ueber die Differentiirbarkeit eines Integrales nach der oberen Grenze. JFM 25.0478.01Thomae, J. 2 1893 Elementary theory of analytic functions of a complex variable. (Elementare Theorie der analytischen Functionen einer complexen Veränderlichen.) JFM 12.0306.01Thomae, J. 3 1880 On the Functions which are represented by series of the form: \[ 1+\frac p1\;\frac {p'}{q'}\;\frac {p''}{q''} +\frac p1\;\frac {p+1}2\;\frac {p'}{q'}\;\frac {p'+1}{q'+1}\;\frac {p''}{q''}\;\frac {p''+1}{q''+1} +\dotsm . \]. (Ueber die Functionen, welche durch Reihen von der Form dargestellt werden: \[ 1+\frac p1\;\frac {p'}{q'}\;\frac {p''}{q''} +\frac p1\;\frac {p+1}2\; \frac {p'}{q'}\;\frac {p'+1}{q'+1}\;\frac {p''}{q''}\;\frac {p''+1}{q''+1} +\dotsm . \].) JFM 11.0336.02Thomae, J. 14 1879 Theorems from the theory of functions. (Sätze aus der Functionentheorie.) JFM 10.0278.01Thomae, J. 2 1878 Integration by parts. (Die partielle Integration.) JFM 07.0145.02Thomae, J. 1 1875 Introduction to the theory of definite integrals. Halle, Nebert. Recension by P. du Bois Raymond. (Einleitung in die Theorie der bestimmten Integrale. Halle, Nebert. Recension von P. du Bois-Raymond.) JFM 07.0153.01Thomae, J. 1 1875 Outline of a theory of complex functions and of theta functions of one variable. (Abriss einer Theorie der complexen Functionen und der Thetafunctionen einer Veränderlichen.) JFM 05.0218.01Thomae, J. 8 1873 On the limits of convergence and divergence of infinite series with positive terms. (Sur les limites de la convergence et de la divergence des séries infinies à termes positifs.) JFM 04.0100.01Thomae, J. 1 1871 Contribution to the determination of \(\vartheta(0,0,\ldots,0)\) by the class modules of algebraic functions. (Beitrag zur Bestimmung von \(\vartheta (0, 0,\dots 0)\) durch die Klassenmoduln algebraischer Funktionen.) JFM 02.0244.01Thomae, J. 22 1870 On the higher hypergeometric series, in particular on the series: \[ 1+\frac{a_{0}a_{1}a_{2}}{1\cdot b_{1}b_{2}}x+\frac{a_{0}(a_{0}+1)a_{1}(a_{1}+1)a_{2}(a_{2}+1)}{1\cdot 2\cdot b_{1}(b_{1}+1)b_{2}(b_{2}+1)}\;x^{2}+\cdots\,. \]. (Ueber die höheren hypergeometrischen Reihen, insbesondere über die Reihe: \[ 1+\frac{a_{0}a_{1}a_{2}}{1\cdot b_{1}b_{2}}x+\frac{a_{0}(a_{0}+1)a_{1}(a_{1}+1)a_{2}(a_{2}+1)}{1\cdot 2\cdot b_{1}(b_{1}+1)b_{2}(b_{2}+1)}\;x^{2}+\cdots\,. \].) JFM 02.0122.01Thomae, J. 12 1870 The higher Heine series, or series \(F(a,a',..a^{(h)},b',..b^{(h)},q,x)\). (Les séries Heinéennes supérieures, ou les séries \(F(a, a', ..a^{(h)}, b', .. b^{(h)}, q, x)\).) JFM 03.0108.01Thomae, J. 7 1870 Sketch of a Theory of complex functions and of theta functions of one variable. (Abriss einer Theorie der complexen Funktionen und der Thetafunktionen einer Veränderlichen.) JFM 02.0187.01Thomae, J. 1 1870 Outline of a theory of complex functions and of the theta functions of one variable. (Abriss einer Theorie der complexen Funktionen und der Thetafunktionen einer Veränderlichen.) JFM 02.0220.02Thomae, J. 1 1870 Contributions to the theory of functions representable by Heine’s series \[ 1+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{b}}{1-q^{c}}x+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{a+1}}{1 q}\cdot\frac{1-q^{b}}{1-q^{c}}\cdot\frac{1-q^{b+1}}{1-q^{c+1}}x^{2}+\ldots \]. (Beiträge zur Theorie der durch die Heine’sche Reihe \[ 1+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{b}}{1-q^{c}}x+\frac{1-q^{a}}{1-q}\cdot\frac{1-q^{a+1}}{1-q}\cdot\frac{1-q^{b}}{1-q^{c}}\cdot\frac{1-q^{b+1}}{1-q^{c+1}}x^{2}+\ldots \] darstellbaren Functionen.) JFM 02.0122.04Thomae, J. 47 1869 Bestimmung von \(d\lg\vartheta(0,0,\ldots 0)\) durch die Classenmoduln. ERAM 066.1717cjThomae, J. 4 1866 all cited Publications top 5 cited Publications all top 5 Cited by 154 Authors 8 Area, Iván 4 Godoy, Eduardo Paciência 4 Masjed-Jamei, Mohammad 4 Mishev, Ilia D. 3 Cao, Jian 3 Ciesielski, Krzysztof Chris 3 Enolskiĭ, Viktor Zelikovich 3 Krattenthaler, Christian Friedrich 3 Nieto Roig, Juan Jose 3 Zemel, Shaul 2 Agrawal, Purshottam Narain 2 Alzer, Horst 2 Arjika, Sama 2 Beukers, Frits 2 Ernst, Thomas 2 Green, Richard M. 2 Guàrdia, Jordi 2 Hahn, Wolfgang 2 Karp, Dmitriĭ Borisovich 2 Karsli, Harun 2 Kopeliovich, Yaacov 2 Mishra, Vishnu Narayan 2 Patel, Prashantkumar Gordhanbhai 2 Prasad, Badri Nath 2 Prilepkina, Elena Gumarovna 2 Soleyman, Fatemeh 2 Soylemez, Dilek 2 Srivastava, Hari Mohan 2 Stade, Eric 2 Ünver, Mehmet 2 Zhou, Hongli 1 Accola, Robert D. M. 1 Acu, Ana Maria 1 Agrawal, Sarita 1 Aktuglu, Huseyin 1 Albayrak, Durmuş 1 Allahviranloo, Tofigh 1 Ashok, Sujay K. 1 Atakishiev, Natig M. 1 Basak, Inna 1 Bernatska, Julia 1 Biermann, Otto 1 Billó, Marco 1 Bowman, Douglas C. 1 Burn, Robert Pemberton 1 Choi, Geumlan 1 Ciucu, Mihai 1 Dauben, Joseph Warren 1 de Jong, Robin 1 del Angel, Pedro Luis 1 Dell’aquila, Eleonora 1 Detlefsen, Michael E. 1 Dimitrov, Dimitar K. 1 Dugac, Pierre 1 Duverney, Daniel 1 Ebin, David G. 1 Ebisu, Akihito 1 Ehrlich, Philip 1 Eilers, Keno 1 Eisenkölbl, Theresia 1 Elmonser, Hédi Ben 1 Epple, Moritz 1 Essadiq, Abderrahman 1 Farkas, Hershel M. 1 Fedorov, Yuri N. 1 Fiorentino, Alessio 1 Formichella, Marc 1 Frau, Marialuisa 1 Gasper, George Jun 1 Ghanmi, Allal 1 Gispert, Hélène 1 Glatzer, Timothy 1 González-Diez, Gabino 1 Grant, David R. 1 Grava, Tamara 1 Gray, Jeremy 1 Hackmann, Eva 1 Hajja, Mowaffaq 1 Han, Yong 1 Heckman, Gert 1 Henstock, Ralph 1 Hıra, Fatma 1 Intissar, Ahmed 1 Iwasaki, Katsunori 1 John, Renjan Rajan 1 Johnson, Dale M. 1 Jouhet, Frédéric 1 Kagramanova, Valeria 1 Kajla, Arun 1 Kalantarova, Habiba V. 1 Kedlaya, Kiran Sridhara 1 Keller, Ott-Heinrich 1 Kim, Jang Soo 1 Kim, Taekyun 1 Kumar, Abhishek 1 Kumar, Dharmendra 1 Kunz, Jutta 1 Lämmerzahl, Claus 1 Lario, Joan-Carles 1 Lê, François ...and 54 more Authors all top 5 Cited in 76 Serials 8 Journal of Mathematical Analysis and Applications 7 The Ramanujan Journal 5 Archive for History of Exact Sciences 5 Letters in Mathematical Physics 4 Mathematische Nachrichten 3 Journal d’Analyse Mathématique 3 Applied Mathematics and Computation 3 Transactions of the American Mathematical Society 3 Historia Mathematica 3 Advances in Difference Equations 2 Acta Mathematica 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Combinatorial Theory. Series A 2 Journal of Computational and Applied Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Bulletin des Sciences Mathématiques 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 American Mathematical Monthly 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematische Semesterberichte 1 Rocky Mountain Journal of Mathematics 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Fortschritte der Physik 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Arithmetica 1 Acta Mathematica Vietnamica 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Demonstratio Mathematica 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of Number Theory 1 Journal of Pure and Applied Algebra 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Notre Dame Journal of Formal Logic 1 Proceedings of the American Mathematical Society 1 Quaestiones Mathematicae 1 Quarterly of Applied Mathematics 1 Real Analysis Exchange 1 Advances in Applied Mathematics 1 Applied Numerical Mathematics 1 Aequationes Mathematicae 1 Bulletin of the American Mathematical Society. New Series 1 Archive for Mathematical Logic 1 Russian Journal of Mathematical Physics 1 Turkish Journal of Mathematics 1 Filomat 1 Integral Transforms and Special Functions 1 Journal of Difference Equations and Applications 1 Arab Journal of Mathematical Sciences 1 Abstract and Applied Analysis 1 Soft Computing 1 Journal of Inequalities and Applications 1 Fractional Calculus & Applied Analysis 1 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics 1 LMS Journal of Computation and Mathematics 1 Regular and Chaotic Dynamics 1 Lobachevskii Journal of Mathematics 1 Journal of Nonlinear Mathematical Physics 1 Fixed Point Theory and Applications 1 The College Mathematics Journal 1 Tbilisi Mathematical Journal 1 Journal of Nonlinear Science and Applications 1 International Journal of Nonlinear Analysis and Applications 1 Analysis and Mathematical Physics 1 Research in Number Theory 1 Mathematical Foundations of Computing all top 5 Cited in 38 Fields 52 Special functions (33-XX) 22 Algebraic geometry (14-XX) 17 Number theory (11-XX) 15 Difference and functional equations (39-XX) 12 Combinatorics (05-XX) 12 Real functions (26-XX) 11 History and biography (01-XX) 11 Ordinary differential equations (34-XX) 10 Approximations and expansions (41-XX) 9 Functions of a complex variable (30-XX) 7 Several complex variables and analytic spaces (32-XX) 4 General and overarching topics; collections (00-XX) 4 Mathematical logic and foundations (03-XX) 4 Integral transforms, operational calculus (44-XX) 3 Sequences, series, summability (40-XX) 3 Quantum theory (81-XX) 2 Field theory and polynomials (12-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Partial differential equations (35-XX) 2 General topology (54-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 \(K\)-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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