Two double-angle formulas of generalized trigonometric functions

Generalized Trigonometric Functions: 10744

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Inequalities involving generalized trigonometric and hyperbolic functions

The Huygens-Wilker type inequalities involving generalized trigonometric functions and generalized hyperbolic functions are established. The first and the second inequalities of Huygens and Wilker, for classes of functions under discussion, are also investigated.

Some Asymptotic Formulas on Generalized Divisor Functions

1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...

Stability of Trigonometric Functional Equations in Generalized Functions

New estimates of double trigonometric sums with exponential functions

We establish a new bound for the exponential sum x∈X y∈Y γ(y) exp(2πiaλ xy /p) , where λ is an element of the residue ring modulo a large prime number p, X and Y are arbitrary subsets of the residue ring modulo p − 1 and γ(n) are any complex numbers with |γ(n)| ≤ 1. In particular, we improve several previously known bounds.