REFINEMENT ON AN INEQUALITY INVOLVING π AND E
Abstract
In this note, we refine the famous inequality $\pi^e < e^\pi$ by adopting an integral approach. Using the same approach, we derive another elegant inequality involving $\pi$ and $e$. The proofs require only basic integral concepts and standard logarithmic inequalities, and are of pedagogical interest. Additionally, a double inequality for the logarithmic function is established.
Fields of Study & Subjects
Mathematical Inequalities and Applications
Analytic and geometric function theory
Mathematics and Applications
Publication details
- Journal / source
- Journal of Computer Science and Applied Mathematics
- Volume
- 7
- Issue
- 2
- Pages
- 41–46
- Publication date
- 1 January 2026