In 1992, Jonathan Borwein and Mark Limber used the first thousand Euler numbers to calculate to 5, 263 decimal places with the Leibniz formula.
12.
These identities show that the quotient of Bernoulli and Euler numbers at the beginning of this section is just the special case of } } when is even.
13.
The Bernoulli numbers and Euler numbers are best understood as " special views " of these numbers, selected from the sequence and scaled for use in special applications.
14.
These identities make it easy to compute the Bernoulli and Euler numbers : the Euler numbers are given immediately by and the Bernoulli numbers are obtained from by some easy shifting, avoiding rational arithmetic.
15.
These identities make it easy to compute the Bernoulli and Euler numbers : the Euler numbers are given immediately by and the Bernoulli numbers are obtained from by some easy shifting, avoiding rational arithmetic.
16.
Orientation-free metrics of a group of connected or surrounded pixels include the Euler number, the perimeter, the area, the compactness, the area of holes, the minimum radius, the maximum radius.
17.
For closed smooth manifolds, the Euler characteristic coincides with the "'Euler number "', i . e ., the Euler class of its tangent bundle evaluated on the fundamental class of a manifold.
18.
Basically, how does one show that the explicit formula ( s ) of the Euler numbers ( given in the article ) define the coefficients of the Taylor series of the secant function ( up to a change in sign )?
19.
If " M " is a Seifert fiber space, then " M " virtually fibers if and only if the rational Euler number of the Seifert fibration or the ( orbifold ) Euler characteristic of the base space is zero.
20.
It expresses the relationship between a local pressure drop e . g . over a restriction and the kinetic energy per volume, and is used to characterize losses in the flow, where a perfect frictionless flow corresponds to an Euler number of 0.
