beta Function

private elemental function beta(mode)

Coefficient beta from the recursive formulation of Legendre polynomials, for the Legendre mode 'mode'.

$$L_n(x) = \alpha \cdot x \cdot L_{n-1}(x) + \beta \cdot L_{n-2}(x)$$

For Legendre polynomials we have:

$$\beta = \frac{1 - n}{n}$$

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	mode	The Legendre mode to compute $\beta$ for.

Return Value real(kind=rk)