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Thomae, Carl Johannes

Author ID: thomae.johannes Recent zbMATH articles by "Thomae, Carl Johannes"
Published as: Thomae, J.; Thomae, Joh.; Thomae, Carl Johannes; Thomae, Johannes
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

Publications by Year

Citations contained in zbMATH Open

19 Publications have been cited 118 times in 105 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 02.0122.04
Thomae, J.
38
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 02.0244.01
Thomae, 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 11.0336.02
Thomae, J.
12
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 02.0122.01
Thomae, J.
11
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 05.0218.01
Thomae, 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 03.0108.01
Thomae, J.
6
1870
Bestimmung von \(d\lg\vartheta(0,0,\ldots 0)\) durch die Classenmoduln. ERAM 066.1717cj
Thomae, J.
4
1866
Elementary theory of analytic functions of a complex variable. (Elementare Theorie der analytischen Functionen einer complexen Veränderlichen.) JFM 12.0306.01
Thomae, 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 29.0334.01
Thomae, J.
2
1898
Ueber die Differentiirbarkeit eines Integrales nach der oberen Grenze. JFM 25.0478.01
Thomae, J.
2
1893
Theorems from the theory of functions. (Sätze aus der Functionentheorie.) JFM 10.0278.01
Thomae, J.
2
1878
Dreieck aus den Mittelloten der Seiten bis zum Umkreismittelpunkt zu konstruieren. JFM 44.0597.01
Thomae, J.
1
1913
Gedankenlose Denker. Eine Ferienplauderei. JFM 37.0062.04
Thomae, J.
1
1906
Projektiver Beweis einiger elementaren Sätze aus der Theorie der ebenen Kurven dritter Ordnung. JFM 33.0566.01
Thomae, J.
1
1902
Ueber den Zusammenhang zwischen den Steiner’schen und den Poncelet’schen Polygonen. JFM 26.0620.01
Thomae, J.
1
1895
Die Kegelschnitte in rein projectiver Behandlung. JFM 25.0986.04
Thomae, Joh.
1
1894
Integration by parts. (Die partielle Integration.) JFM 07.0145.02
Thomae, 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 04.0100.01
Thomae, 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 02.0187.01
Thomae, J.
1
1870
Dreieck aus den Mittelloten der Seiten bis zum Umkreismittelpunkt zu konstruieren. JFM 44.0597.01
Thomae, J.
1
1913
Gedankenlose Denker. Eine Ferienplauderei. JFM 37.0062.04
Thomae, J.
1
1906
Projektiver Beweis einiger elementaren Sätze aus der Theorie der ebenen Kurven dritter Ordnung. JFM 33.0566.01
Thomae, 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 29.0334.01
Thomae, J.
2
1898
Ueber den Zusammenhang zwischen den Steiner’schen und den Poncelet’schen Polygonen. JFM 26.0620.01
Thomae, J.
1
1895
Die Kegelschnitte in rein projectiver Behandlung. JFM 25.0986.04
Thomae, Joh.
1
1894
Ueber die Differentiirbarkeit eines Integrales nach der oberen Grenze. JFM 25.0478.01
Thomae, J.
2
1893
Elementary theory of analytic functions of a complex variable. (Elementare Theorie der analytischen Functionen einer complexen Veränderlichen.) JFM 12.0306.01
Thomae, 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 11.0336.02
Thomae, J.
12
1879
Theorems from the theory of functions. (Sätze aus der Functionentheorie.) JFM 10.0278.01
Thomae, J.
2
1878
Integration by parts. (Die partielle Integration.) JFM 07.0145.02
Thomae, 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 05.0218.01
Thomae, 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 04.0100.01
Thomae, 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 02.0244.01
Thomae, 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 02.0122.01
Thomae, J.
11
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 03.0108.01
Thomae, J.
6
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 02.0187.01
Thomae, 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 02.0122.04
Thomae, J.
38
1869
Bestimmung von \(d\lg\vartheta(0,0,\ldots 0)\) durch die Classenmoduln. ERAM 066.1717cj
Thomae, J.
4
1866
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Cited by 137 Authors

7 Area, Iván
4 Godoy, Eduardo Paciência
3 Enolskiĭ, Viktor Zelikovich
3 Krattenthaler, Christian Friedrich
3 Masjed-Jamei, Mohammad
3 Zemel, Shaul
2 Alzer, Horst
2 Beukers, Frits
2 Ciesielski, Krzysztof Chris
2 Ernst, Thomas
2 Green, Richard M.
2 Guàrdia, Jordi
2 Hahn, Wolfgang
2 Karp, Dmitriĭ Borisovich
2 Kopeliovich, Yaacov
2 Mishev, Ilia D.
2 Mishra, Vishnu Narayan
2 Nieto Roig, Juan Jose
2 Patel, Prashantkumar G.
2 Prasad, Badri Nath
2 Prilepkina, Elena Gumarovna
2 Srivastava, Hari Mohan
2 Stade, Eric
1 Accola, Robert D. M.
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 Burn, Robert Pemberton
1 Cao, Jian
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 Gispert, Hélène
1 Glatzer, Timothy
1 González-Diez, Gabino
1 Grava, Tamara
1 Gray, Jeremy John
1 Hackmann, Eva
1 Hajja, Mowaffaq
1 Han, Yong
1 Heckman, Gert
1 Henstock, Ralph
1 Iwasaki, Katsunori
1 John, Renjan Rajan
1 Johnson, Dale M.
1 Jouhet, Frédéric
1 Kagramanova, Valeria
1 Kalantarova, Habiba V.
1 Karsli, Harun
1 Keller, Ott-Heinrich
1 Kim, Jang Soo
1 Kim, Taekyun
1 Kunz, Jutta
1 Lämmerzahl, Claus
1 Lario, Joan-Carles
1 Lê, François
1 Lerda, Alberto
1 Liu, Zhi-Guo
1 Maier, Robert S.
1 Marcellán Español, Francisco
1 Milio, Enea
1 Moreno-Balcázar, Juan José
1 Müller-Stach, Stefan J.
1 Murthy, K. Narasimha
1 Nagano, Atsuhira
1 Nart, Enric
1 Noeiaghdam, Zahra
1 Nørlund, Niels Erik
1 Novick-Cohen, Amy
1 Ozarslan, Mehmet Ali
1 Park, SeungKyung
1 Parker, John R.
1 Phothi, Supaluk
...and 37 more Authors
all top 5

Cited in 67 Serials

6 Journal of Mathematical Analysis and Applications
6 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
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 Advances in Difference Equations
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 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 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 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 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 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 Analysis and Mathematical Physics
1 Research in Number Theory
all top 5

Cited in 38 Fields

43 Special functions (33-XX)
22 Algebraic geometry (14-XX)
14 Number theory (11-XX)
12 Difference and functional equations (39-XX)
11 History and biography (01-XX)
11 Ordinary differential equations (34-XX)
10 Real functions (26-XX)
9 Functions of a complex variable (30-XX)
8 Combinatorics (05-XX)
7 Several complex variables and analytic spaces (32-XX)
6 Approximations and expansions (41-XX)
4 General and overarching topics; collections (00-XX)
3 Mathematical logic and foundations (03-XX)
3 Partial differential equations (35-XX)
3 Integral transforms, operational calculus (44-XX)
3 Quantum theory (81-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Group theory and generalizations (20-XX)
2 Measure and integration (28-XX)
2 General topology (54-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Field theory and polynomials (12-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 Sequences, series, summability (40-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

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