اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدTwo double-angle formulas of generalized trigonometric functions
67
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
With respect to generalized trigonometric functions, since the discovery of double-angle formula for a special case by Edmunds, Gurka and Lang in 2012, no double-angle formulas have been found. In this paper, we will establish new double-angle formulas of generalized trigonometric functions in two special cases.
قيم البحث
اقرأ أيضاً
Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator. Compared to GTFs with one parame
ter, there are few applications of GTFs with two parameters to differential equations. We will apply GTFs with two parameters to studies on the inviscid primitive equations of oceanic and atmospheric dynamics, new formulas of Gaussian hypergeometric functions, and the $L^q$-Lyapunov inequality for the one-dimensional $p$-Laplacian.
In this paper we will establish some double-angle formulas related to the inverse function of $int_0^x dt/sqrt{1-t^6}$. This function appears in Ramanujans Notebooks and is regarded as a generalized version of the lemniscate function.
It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties fo
r the other. In this way, Mitrinovi{c}-Adamovi{c}-type inequalities, multiple-angle formulas, and double-angle formulas for both can be produced.
Famous Redheffers inequality is generalized to a class of anti-periodic functions. We apply the novel inequality to the generalized trigonometric functions and establish several Redheffer-type inequalities for these functions.
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning commutation with rotation, continu
ation beyond the domain of univalence, and periodicity.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
