Does anybody recognize this notation?
I know the two dots means annuity due, the s refers to future value, but I'm not sure about the rest.
I'm assuming that the latter value (without the (m)) refers to:
$$\sum_{k=0}^{40-1}(1+i)^k\space _kp_{25}$$
If the formula I have provided above is correct, how can I represent the former in the form of the latter (referring to the two values in the image)?
$$\ddot s_{25 : \overline{40}\rceil}^{(m)}$$ is the accumulated value of a life annuity-due for a life aged $25$, of an amount $1/m$ paid $m$ times per year, for $40$ years or until death, whichever occurs first. An effective annual rate of interest $i$ is implied. Consequently, $$\ddot s_{25 : \overline{40}\rceil}^{(m)} = \sum_{k=0}^{40-1} \frac{1}{m} \left(1 + \frac{i^{(m)}}{m}\right)^{\!40-k} {}_k p_{25},$$ where $i^{(m)}$ is the nominal $m$-thly rate of interest.