Theta function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Theta function" in English language version.

refsWebsite

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8doi.org

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3wolfram.com

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2arxiv.org

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2stackexchange.com

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1nist.gov

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1uni-bonn.de

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1mpmath.org

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1projecteuclid.org

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1msu.edu

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arxiv.org

Tyurin, Andrey N. (30 October 2002). "Quantization, Classical and Quantum Field Theory and Theta-Functions". arXiv:math/0210466v1.
Berndt, Bruce C; Rebák, Örs (9 January 2022). "Explicit Values for Ramanujan's Theta Function ϕ(q)". Hardy-Ramanujan Journal. 44: 8923. arXiv:2112.11882. doi:10.46298/hrj.2022.8923. S2CID 245851672.

doi.org

Tata Lectures on Theta I. Modern Birkhäuser Classics. Boston, MA: Birkhäuser Boston. 2007. p. 4. doi:10.1007/978-0-8176-4577-9. ISBN 978-0-8176-4572-4.
Yi, Jinhee (2004). "Theta-function identities and the explicit formulas for theta-function and their applications". Journal of Mathematical Analysis and Applications. 292 (2): 381–400. doi:10.1016/j.jmaa.2003.12.009.
Berndt, Bruce C; Rebák, Örs (9 January 2022). "Explicit Values for Ramanujan's Theta Function ϕ(q)". Hardy-Ramanujan Journal. 44: 8923. arXiv:2112.11882. doi:10.46298/hrj.2022.8923. S2CID 245851672.
Yi, Jinhee (15 April 2004). "Theta-function identities and the explicit formulas for theta-function and their applications". Journal of Mathematical Analysis and Applications. 292 (2): 381–400. doi:10.1016/j.jmaa.2003.12.009.
Mező, István (2013), "Duplication formulae involving Jacobi theta functions and Gosper's $q$ -trigonometric functions", Proceedings of the American Mathematical Society, 141 (7): 2401–2410, doi:10.1090/s0002-9939-2013-11576-5
Mező, István (2012). "A $q$ -Raabe formula and an integral of the fourth Jacobi theta function". Journal of Number Theory. 133 (2): 692–704. doi:10.1016/j.jnt.2012.08.025. hdl:2437/166217.
Mahlburg, Karl (2004). "The overpartition function modulo small powers of 2". Discrete Mathematics. 286 (3): 263–267. doi:10.1016/j.disc.2004.03.014.
Kim, Byungchan (28 April 2009). "Elsevier Enhanced Reader". Discrete Mathematics. 309 (8): 2528–2532. doi:10.1016/j.disc.2008.05.007.

handle.net

hdl.handle.net

Mező, István (2012). "A $q$ -Raabe formula and an integral of the fourth Jacobi theta function". Journal of Number Theory. 133 (2): 692–704. doi:10.1016/j.jnt.2012.08.025. hdl:2437/166217.

mpmath.org

"Number-theoretical, combinatorial and integer functions – mpmath 1.1.0 documentation". Retrieved 2021-07-18.

msu.edu

archive.lib.msu.edu

"Elliptic Integral Singular Value". msu.edu. Retrieved 2023-04-07.

nist.gov

dlmf.nist.gov

See e.g. https://dlmf.nist.gov/20.1. Note that this is, in general, not equivalent to the usual interpretation $(e^{z})^{\alpha }=e^{\alpha \operatorname {Log} e^{z}}$ when $z$ is outside the strip $-\pi <\operatorname {Im} z\leq \pi$ . Here, $\operatorname {Log}$ denotes the principal branch of the complex logarithm.

oeis.org

"A000009 - OEIS". 2022-03-09.

projecteuclid.org

Ohyama, Yousuke (1995). "Differential relations of theta functions". Osaka Journal of Mathematics. 32 (2): 431–450. ISSN 0030-6126.

researchgate.net

Ramanujan's theta-function identities involving Lambert series

semanticscholar.org

api.semanticscholar.org

Berndt, Bruce C; Rebák, Örs (9 January 2022). "Explicit Values for Ramanujan's Theta Function ϕ(q)". Hardy-Ramanujan Journal. 44: 8923. arXiv:2112.11882. doi:10.46298/hrj.2022.8923. S2CID 245851672.

springer.com

link.springer.com

Tata Lectures on Theta I. Modern Birkhäuser Classics. Boston, MA: Birkhäuser Boston. 2007. p. 4. doi:10.1007/978-0-8176-4577-9. ISBN 978-0-8176-4572-4.

stackexchange.com

math.stackexchange.com

"integration - Curious integrals for Jacobi Theta Functions $\int_0^1 \vartheta_n(0,q)dq$". 2022-08-13.

codegolf.stackexchange.com

"code golf - Strict partitions of a positive integer". Retrieved 2022-03-09.

uni-bonn.de

www-elsa.physik.uni-bonn.de

Andreas Dieckmann: Table of Infinite Products Infinite Sums Infinite Series, Elliptic Theta. Physikalisches Institut Universität Bonn, Abruf am 1. Oktober 2021.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Elliptic Alpha Function". MathWorld.
Eric W. Weisstein (2022-03-11). "Partition Function P".
Eric W. Weisstein (2022-03-11). "Partition Function Q".

worldcat.org

Ohyama, Yousuke (1995). "Differential relations of theta functions". Osaka Journal of Mathematics. 32 (2): 431–450. ISSN 0030-6126.