"Relations and Functions" stand out as crucial topics within algebra. These terms, though related, hold distinct mathematical meanings. It's common to feel uncertain about their disparities. To ...

Let Fn be a free group of rank n with free basis x1, ⋯, xn. Let {y1, ⋯, yk} be a set of k ≤ n elements of Fn, where each yi is represented by a word Yi(x1, ⋯, xn) in the generators xj. Let ∂ yi/∂ xj ...

In the paper, the authors find series expansions and identities for positive integer powers of inverse (hyperbolic) sine and tangent, for composite of incomplete gamma function with inverse hyperbolic ...

Composite functions are made when the output from one function is used as the input of another function. The names of the functions are written next to each other, with the function that is used first ...