Function that calculates the sum of higher order terms, cn(ℓ), provided by ldep from ℓmin to ∞.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer(kind=ip), | intent(in) | :: | lmin | The value of ℓ at which to start the sum, ℓmin. |
||
| integer(kind=ip), | intent(in) | :: | order | The order of the higher order term, n. |
The return value is ∞∑ℓ=ℓmincn(ℓ)={ℓmin4ℓ2min−1,n=2ℓmin48ℓ4min−120ℓ2min+27,n=3ℓmin5(64ℓ6min−560ℓ4min+1036ℓ2min−225),n=4.
function lsum ( lmin, order )
!! Function that calculates the sum of higher order terms, \(c_n(\ell)\),
!! provided by [[ldep]] from \(\ell_{\mathrm{min}}\) to \(\infty\).
integer(ip), intent(in) :: lmin
!! The value of \(\ell\) at which to start the sum,
!! \(\ell_{\mathrm{min}}\).
integer(ip), intent(in) :: order
!! The order of the higher order term, \(n\).
real(wp) :: lsum
!! The return value is \[\sum_{\ell=\ell_{\mathrm{min}}}^{\infty} c_n(\ell) =
!! \begin{cases}
!! \frac{\ell_{\mathrm{min}}}{4\ell_{\mathrm{min}}^2-1}, & n=2 \\
!! \frac{\ell_{\mathrm{min}}}{48\ell_{\mathrm{min}}^4-
!! 120\ell_{\mathrm{min}}^2+27}, & n=3 \\
!! \frac{\ell_{\mathrm{min}}}{5 (64\ell_{\mathrm{min}}^6-
!! 560\ell_{\mathrm{min}}^4+1036\ell_{\mathrm{min}}^2-225)}, & n=4
!! \end{cases} \].
real(wp) :: lm
lm = real(lmin,wp)
select case (order)
case (2)
lsum = lm/(4.0_wp*lm**2-1.0_wp)
case (4)
lsum = lm/(48.0_wp*lm**4-120.0_wp*lm**2+27.0_wp)
case (6)
lsum = lm/(5.0_wp &
*(64.0_wp*lm**6-560.0_wp*lm**4+1036.0_wp*lm**2-225.0_wp))
case default
stop "error: lsum called with unsupported order"
end select
end function lsum