number e , także: Euler number

The coefficients are the Euler numbers of odd and even index, respectively.

The Euler number is a dimensionless number used in fluid flow calculations.

(It usually differs from the Euler number e defined above.)

Bernoulli numbers can be expressed through the Euler numbers and vice versa.

An explicit formula for Euler numbers is given by:

The odd-indexed Euler numbers are all zero.

The Euler numbers appear as a special value of the Euler polynomials.

These conversion formulas express an inverse relation between the Bernoulli and the Euler numbers.

Computing the Euler number.

Some authors re-index the sequence in order to omit the odd-numbered Euler numbers with value zero, and/or change all signs to positive.

That meant that they had to possess their own immutable mathematical signatures-like the Euler number, only orders of magnitude more complex.

Euler number (physics)

The Euler numbers are a sequence of integers intimately connected with the Bernoulli numbers.

This asymptotic equation reveals that π lies in the common root of both the Bernoulli and the Euler numbers.

In order for two flows to be similar they must have the same geometry, and have equal Reynolds numbers and Euler numbers.

The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions.

You've just discovered the Gauss-Bonnet Theorem, linking the Euler number and total curvature."

These enumerate the number of alternating permutations on n letters and are related to the Euler numbers and the Bernoulli numbers.

The Bernoulli numbers and Euler numbers are best understood as special views of these numbers, selected from the sequence S and scaled for use in special applications.

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.

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.

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 1.

Some of Euler's greatest successes were in applying analytic methods to real world problems, describing numerous applications of Bernoulli's numbers, Fourier series, Venn diagrams, Euler numbers, e and π constants, continued fractions and integrals.

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.

The manifold can be constructed by first plumbing together disc bundles of Euler number 2 over the sphere, according to the Dynkin diagram for E. This results in P'E, a 4-manifold with boundary equal to the Poincare homology sphere.