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Secans
The power series for the secans is
Explanation
The first derivative of the secans is
Only the secans and the tangens appear here. If we calculate more derivatives this will remain unchanged because (tan x)' = sec2x, so that
The point x = 0 gives sec (0) = 1 and tan (0) = 0 so
We substitute this in the Taylor series and find
General format
You can write the power series as a sum
where Un is the n-th up/down number. Or as
where E2n is the n-th Euler number.