Several numbers are named after Euler.
Euler’s number is the irrational number
This is the groupoid cardinality of the groupoid , the core of FinSet.
The Euler numbers , are a sequence of integers defined via the generating function
All odd-numbered members of the sequence vanish: for . , , , see Euler number at wikipedia for more and the Abramowitz–Stegun handbook for many Euler numbers.
Euler numbers generalize to Euler polynomials defined via the generating function
so that . The Euler polynomials satisfy the recursion and may be conversely expressed via Euler numbers as
There is also a complementarity formula . See e.g. Louis Comtet, Advanced combinatorics, D. Reifel Publ. Co., Dordrecht-Holland, Boston 1974 djvu
There are also Eulerian numbers (forming a different, double sequence ).
Revised on May 13, 2010 12:34:55
by Urs Schreiber