Function beta_impl 

pub fn beta_impl<P, E, V, const N: usize>(a: V, b: V, l: &Lanczos<E, N>) -> V
where
    P: Policy,
    E: FloatElementWithBits,
    V: FloatVectorWithBits<Element = E> + SpecializedSpecialMath<E>,

Shared beta implementation for all real element types.

B(a, b) = Gamma(a)Gamma(b)/Gamma(a+b), evaluated from the exp(g)-scaled Lanczos sums directly rather than through three tgamma calls, so the large common factors cancel symbolically instead of overflowing.

Only defined for a, b > 0; anything else is NaN under check_overflow.