e^(na) (valid na^2 << 1), e^(na) e^(-na^2/2) (valid na^3 << 1),
and the difference quotient ((x+d)^n - x^n)/d -> n x^(n-1).
Mirrors morie.fn ch7 appendix modules.
Usage
morie_approx_ladder(a, n, order = 1, x = NULL, delta = NULL, power = 2)
Arguments
- a
perturbation, > -1.
- n
exponent.
- order
1 or 2.
- x, delta
optional difference-quotient inputs.
- power
exponent for the difference quotient.
Value
list: exact, approx, validity, quotient, derivative.
References
Morin (2016), Appendix C, eqs. (7.14), (7.21),
(7.23)-(7.24), (7.31)-(7.35).
Examples
morie_approx_ladder(-1 / 365, 23)$approx
#> [1] 0.9389306
