integral representation in a sentence

Examples

1. The integral representation corresponding to the permutation action on 23 points decomposes into the trivial representation and a 22-dimensional representation.
2. During the studying divergent infinite series Euler met with G via, for example, the above integral representations . survival analysis.
3. Nebe is known for using integral representations of finite groups to construct explicit examples of discrete mathematical structures using computer algebra systems.
4. The integral representation immediately shows that G ( r ) is positive, since it is represented as a weighted sum of positive Gaussians.
5. So in the relativistic case, the Feynman path-integral representation of the propagator includes paths which go backwards in time, which describe antiparticles.
6. In mathematical physics, a Grassmann number, named after Hermann Grassmann, is a mathematical construction which allows a functional integral representation for Fermionic fields.
7. This integral follows from the general relation of the polylogarithm with the Hurwitz zeta function ( see above ) and a familiar integral representation of the latter.
8. then reversing the order of integral and sum, and finally identifying the summands with an integral representation of the upper incomplete gamma function, one obtains:
9. My question is : what is known about such polynomials ( name, generating function, integral representation, roots, differential equations, etc . )?
10.  Using Ergodic methods, Venkatesh, jointly with Jordan Ellenberg, made significant progress on the Hasse principle for integral representations of quadratic forms by quadratic forms.