Does the polynomial sequence of orthonormal polynomials with respect to the inner product $\langle f, g\rangle = \int_0^1 f(x)g(x)\ dx$ of increasing degree have a name? It doesn't seem to be the Legendre polynomials or Jacobi polynomials, but maybe someone else has their name on it.
Explicitly, here's the first few terms: $$\big(1, \sqrt{12}(x-\frac 12), 6\sqrt{5}(x^2-x+\frac 16), \cdots\big)$$
PS, if the answer is no, then I call dibs on the Bobbie D polynomials. ;D
They are the shifted Legendre polynomials