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In this paper the discussion of the effect of trigonometric series on the theory of integration is continued from an earlier paper by Gluchoff, Trigonometric series and theories of integration, Math.Mag., 67 (1994), 3--20.
The well known table of Gradshteyn and Ryzhik contains indefinite and definite integrals of both elementary and special functions. We give proofs of several entries containing integrands with some combination of hyperbolic and trigonometric functions
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
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.
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 formul
We study moduli stabilization and a realization of de Sitter vacua in generalized F-term uplifting scenarios of the KKLT-type anti-de Sitter vacuum, where the uplifting sector X directly couples to the light Kahler modulus T in the superpotential thr