A Polynomial given by the sum

(1) |

(2) | |||

(3) | |||

(4) |

where is a Binomial Coefficient. Setting and normalizing by gives the Euler Number

(5) |

(6) |

(7) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.). ``Bernoulli and Euler Polynomials and the Euler-Maclaurin Formula.''
§23.1 in *Handbook of Mathematical Functions with Formulas,
Graphs, and Mathematical Tables, 9th printing.* New York: Dover, pp. 804-806, 1972.

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, 1979.

Spanier, J. and Oldham, K. B. ``The Euler Polynomials .''
Ch. 20 in *An Atlas of Functions.* Washington, DC: Hemisphere, pp. 175-181, 1987.

© 1996-9

1999-05-25