Several Integrability Formulas of Special Functions

Several Integrability Formulas of Special Functions

In this article, we give several integrability formulas of special and composite functions including trigonometric function, inverse trigonometric function, hyperbolic function and logarithmic function. The notation and terminology used here are introduced in the following papers:

Several Integrability Formulas of Special Functions. Part II

In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, the hyperbolic function and the polynomial function [3]. For simplicity, we adopt the following rules: r, x, a, b denote real numbers, n, m denote elements of N, A denotes a closed-interval subset of R, and Z denotes an open subset of R. One can pr...

Several Differentiation Formulas of Special Functions . Part

(Def. 2) cosec = 1 the function sin . For simplicity, we follow the rules: x, a, b, c are real numbers, n is a natural number, Z is an open subset of R, and f , f1, f2 are partial functions from R to R. One can prove the following propositions: (1) If (the function cos)(x) 6= 0, then sec is differentiable in x and (sec)′(x) = (the function sin)(x) (the function cos)(x)2 . (2) If (the function s...

Several Differentiation Formulas of Special Functions

Several Higher Differentiation Formulas of Special Functions

The notation and terminology used in this paper are introduced in the following articles: [16], [13], [2], [3], [5], [1], [7], [9], [12], [10], [8], [18], [14], [11], [6], [15], and [17]. For simplicity, we use the following convention: x, r, a, x0, p are real numbers, n, i, m are elements of N, Z is an open subset of R, and f , f1, f2 are partial functions from R to R. Next we state a number o...