ترغب بنشر مسار تعليمي؟ اضغط هنا

Ramanujans identities, minimal surfaces and solitons

143   0   0.0 ( 0 )
 نشر من قبل Rukmini Dey Dr.
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English
 تأليف Rukmini Dey




اسأل ChatGPT حول البحث

Using Ramanujans identities and the Weierstrass-Enneper representation of minimal surfaces and the analogue for Born-Infeld solitons, we derive further non-trivial identities.



قيم البحث

اقرأ أيضاً

In this paper, we rewrite two forms of an Euler-Ramanujan identity in terms of certain Dirichlet series and derive functional equation of the latter. We also use the Weierstrass-Enneper representation of minimal surfaces to obtain some identities inv olving these Dirichlet series and one complex parameter.
135 - Md. Shafiul Alam 2021
We study the relation between Hecke groups and the modular equations in Ramanujans theories of signature 2, 3 and 4. The solution $(alpha,beta)$ to the generalized modular equation satisfies a polynomial equation $P(alpha,beta)=0$ and we determine th e degree in each of $alpha$ and $beta$ of the polynomial $P(alpha,beta)$ explicitly. We establish some mutually equivalent statements related to Hecke subgroups and modular equations, and prove that $(1-beta, 1-alpha)$ is also a solution to the generalized modular equation and $P(1-beta, 1-alpha)=0$.
123 - Rukmini Dey , Pradip Kumar 2012
In this paper, we discuss a one parameter family of complex Born-Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B-I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples. We find that the action or the energy of this family of solitons remains invariant in this family and find that the well-known Lorentz symmetry of the B-I equations is responsible for it.
84 - Sidney A. Morris 2020
In 1730 James Stirling, building on the work of Abraham de Moivre, published what is known as Stirlings approximation of $n!$. He gave a good formula which is asymptotic to $n!$. Since then hundreds of papers have given alternative proofs of his resu lt and improved upon it, including notably by Burside, Gosper, and Mortici. However Srinivasa Ramanujan gave a remarkably better asymptotic formula. Hirschhorn and Villarino gave a nice proof of Ramanujans result and an error estimate for the approximation. In recent years there have been several improvements of Stirlings formula including by Nemes, Windschitl, and Chen. Here it is shown (i) how all these asymptotic results can be easily verified; (ii) how Hirschhorn and Villarinos argument allows a tweaking of Ramanujans result to give a better approximation; (iii) that a new asymptotic formula can be obtained by further tweaking of Ramanujans result; (iv) that Chens asymptotic formula is better than the others mentioned here, and the new asymptotic formula is comparable with Chens.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا