اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRamanujans identities, minimal surfaces and solitons
143
0
0.0
(
0
)
تأليف
Rukmini Dey
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
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 $P(1-beta, 1-alpha)=0$.
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.
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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
