Euler Numbers

in mathematics, the integers E_n that are the coefficients of tⁿ/n! in the expansion of the function 1/cosh t in the power series

These numbers, which were introduced by L. Euler in 1755, are related by the formula (E + 1)ⁿ + (E – 1)ⁿ = 0, n = 1, 2, 3, . . ., E₀ = 1 (after raising to the power, E_k must be inserted for E^k). The following relations hold between Euler numbers and Bernoulli numbers:

Euler numbers are encountered in various formulas of mathematical analysis.

单词	euler numbers
释义	Euler Numbers Euler Numbers in mathematics, the integers E_n that are the coefficients of tⁿ/n! in the expansion of the function 1/cosh t in the power series These numbers, which were introduced by L. Euler in 1755, are related by the formula (E + 1)ⁿ + (E – 1)ⁿ = 0, n = 1, 2, 3, . . ., E₀ = 1 (after raising to the power, E_k must be inserted for E^k). The following relations hold between Euler numbers and Bernoulli numbers: Euler numbers are encountered in various formulas of mathematical analysis.
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