| 1. | Bernoulli numbers can be expressed through the Euler numbers and vice versa.
|
| 2. | The coefficients are the Euler numbers of odd and even index, respectively.
|
| 3. | These conversion formulas express an inverse relation between the Bernoulli and the Euler numbers.
|
| 4. | The in the expansion of are Euler numbers.
|
| 5. | The name Euler numbers in particular is sometimes used for a closely related sequence.
|
| 6. | The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions.
|
| 7. | This asymptotic equation reveals that lies in the common root of both the Bernoulli and the Euler numbers.
|
| 8. | The errors can in fact be predicted; they are generated by the Euler numbers according to the asymptotic formula
|
| 9. | See and . ( ) / ( ) are the second ( fractional ) Euler numbers and an autosequence of the second kind.
|
| 10. | These enumerate the number of alternating permutations on " n " letters and are related to the Euler numbers and the Bernoulli numbers.
|
