A quick question. Given a boundary condition that a function $f(x)=\sum_{n=0}^\infty a_n P_{2n+1}(x)$ , which is defined for $x$ in $[0,1]$, not for $-1$ to $1$.
I know the standard Fourier- Legendre Series, but in this question, the Legendre polynomials only have its odd terms, together with x only defined in $[0,1]$. In this case, how to write $f(x)$ in terms of integral from 1 to 0 ?