Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of ...

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 ...

Abstract: In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier ...

Abstract: In this paper, we derive a relation for the circular convolution operation in the discrete sine and cosine transform domains. The transform coefficients are either symmetric or asymmetric ...

In the study of circular functions, the unit circle plays a central role in linking angles with trigonometric values. By defining sine, cosine, and tangent in terms of coordinates on a circle of ...

This section focuses on the key features and methods for working with linear graphs. It demonstrates how to sketch graphs from rules, derive rules from graphs, and calculate key features such as the ...