4 citations · 8 across the 10 of their papers we have counts for
10 papers
Less Mundane Applications of the Most Mundane Functions
Pisheng Ding
Linear functions are arguably the most mundane among all functions. However, the basic fact that a multi-variable linear function has a constant gradient field can provide simple g…
Real-Analyticity of Generalized Sine Functions with Two Parameters
Pisheng Ding
We identify the maximal real interval on which is real-analytic for any real number and any integer . We achieve this by first proving that is…
Generalized Sine Functions, Complexified
Pisheng Ding, Sunil K. Chebolu
Generalized sine and cosine functions, and , that parametrize the generalized unit circle are, much like their classical circular counterparts, ext…
A Fundamental Theorem of Calculus for Second-order Directional Derivative
Pisheng Ding
Given a two-variable function without critical points and a compact region bounded by two level curves of , this note proves that the integral over of the second-ord…
Analytic Continuation of Generalized Trigonometric Functions
Pisheng Ding
Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some…
On the Gradient of Harmonic Functions
Pisheng Ding
For a harmonic function u on Euclidean space, this note shows that its gradient is essentially determined by the geometry of its level hypersurfaces. Specifically, the factor by wh…