Name
Abstract | ||
|---|---|---|
An identity stated by Kimura and proved by Ruehr, Kimura and others stipulates that for any function $f$ continuous on $[-\frac{1}{2}, \frac{3}{2}]$ one has $$ \int_{-1/2}^{3/2} f(3x^2 - 2x^3) dx = 2 \int_0^1 f(3x^2 - 2x^3) dx. $$ We prove that this equality is not an isolated example by providing a family of polynomials, related to the Tchebychev polynomials and of which $(3x^2 - 2x^3)$ is a particular case, giving rise to similar identities. |
Year | Venue | DocType |
|---|---|---|
2018 | Integers | Journal |
Volume | Citations | PageRank |
18A | 0 | 0.34 |
References | Authors | |
0 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jean-Paul Allouche | 1 | 0 | 1.69 |