Results 11 to 20 of about 1,502 (98)

Explicit Evaluations of Cubic and Quartic Theta-Functions [PDF]

ISRN Discrete Mathematics, 2012
We find explicit values of cubic and quartic theta-functions and their quotients by parameterizations. In the process, we also find some transformation formulas of these theta-functions.
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On Ramanujan's general theta function and a generalization of the Borweins' cubic theta functions

Asian-European Journal of Mathematics, 2015
The Borwein brothers have introduced and studied three cubic theta functions. Many generalizations of these functions have been studied as well. In this paper, we introduce a new generalization of these functions and establish general formulas that are connecting our functions and Ramanujan's general theta function.
Adiga, Chandrashekar, Nasser, Bulkhali Saeed Abdo   +1 more
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On the Cubic Theta Function

Nagoya Mathematical Journal, 1987
The generalized theta function of a totally imaginary field including n-th roots of unity, which was defined by T. Kubota [2], was introduced in his investigation of the reciprosity law of the n-th power residue. If n = 2, it reduces to the classical theta function. In the case n = 3 for the Eisenstein field, the Fourier coefficients of the cubic theta
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A new numerical technique for the solution of time-fractional nonlinear Klein–Gordon equation involving Atangana–Baleanu derivative using cubic B-spline functions

Open Physics
One of the earliest attempts to make special relativity and quantum mechanics compatible was the Klein–Gordon equation (KGE). In the 1920s, Oskar Klein and Walter Gordon independently proposed it. This equation plays a very significant role in the fields
Shaheen Muserat, Abbas Muhammad, Abdullah Farah Aini, Hamed Yasser Salah   +3 more
doaj   +1 more source

Differential equations involving cubic theta functions and Eisenstein series

Osaka Journal of Mathematics, 2016
In this paper, we derive systems of ordinary differential equations (ODEs) satisfied by modular forms of level three, which are level three versions of Ramanujan's system of ODEs satisfied by the classical Eisenstein series.
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On Ramanujan's cubic continued fraction and explicit evaluations of theta-functions

, 2004
We study Ramanujan's cubic continued fraction and explicit evaluations of theta ...
Adiga, Chandrashekar, Kim, T., Naika, M. S. M., Madhusudhan, H. S.   +3 more
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On Some Eisenstein Series Identities Associated with Borwein’s Cubic Theta Functions

Indian Journal of Pure and Applied Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On some new Eisenstein series identities involving the Broweins' cubic theta function $a(q)$ and the convolution sum $\ds\sum_{i+3j=m}\sigma(i)\sigma(j)$

Boletim da Sociedade Paranaense de Matemática
In this paper, employing the $(p, k)$-parametrization of Srinivasa Ramanujan's Eisenstein series $L(q), M(q)$ and the Borweins' cubic theta functions due to Alaca et. al \cite{Alaca1, Alaca12, Alaca13}, we derive some new Eisenstein series identities involving the Borweins' cubic theta function $a(q)$ with the help of Computer.
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Structure-function coupling of large-scale cortical networks across the lifespan is spectrally specific. [PDF]

Commun Biol
Picci G, Rempe MP, Petro NM, Son JJ, Casagrande CC, Ott LR, Penhale SH, Embury CM, Schantell M, Johnson HJ, Okelberry HJ, Willett MP, Wang YP, Stephen JM, Calhoun VD, Wiesman AI, Kurz MJ, Heinrichs-Graham E, Wilson TW.   +18 more
europepmc   +1 more source

Comparison of Resting-State EEG and Synchronization Between Young Adults with Down Syndrome and Controls in Bipolar Montage. [PDF]

Brain Sci
Pastor J, Vega-Zelaya L, Real de Asúa D.   +2 more
europepmc   +1 more source