New asymptotic expansions on hyperfactorial functions

Asymptotic Expansions of Certain Partial Theta Functions

We establish an asymptotic expansion for a class of partial theta functions generalizing a result found in Ramanujan’s second notebook. Properties of the coefficients in this more general asymptotic expansion are studied, with connections made to combinatorics and a certain Dirichlet series.

EUCLIDEAN ASYMPTOTIC EXPANSIONS OF GREEN FUNCTIONS OF QUANTUM FIELDS. (I) Expansions of Products of Singular Functions

The problem of asymptotic expansions of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem. It is shown that the problem reduces to studying asymptotic expansions of products of a class of singular functions in the sense of the distribution theory....

Asymptotic Expansions

Asymptotic expansions of functions are useful in statistics in three main ways. Firstly, conventional asymptotic expansions of special functions are useful for approximate computation of integrals arising in statistical calculations. An example given below is the use of Stirling's approximation to the gamma function. Second, asymptotic expansions of density or distribution functions of estimato...

Asymptotic Expansions of Multiple Integrals of Rapidly Oscillating Functions

Expansions of multiple integrals w(aixi,.. .,anxn)g(xi,... ,x„)dxi ■ ■ -dxn, r°i r°n I " Ja\ J a„ where w is a function on R" which is (bk oj,)-periodic in the fcth variable, k = 1,... ,n, and g is smooth, are given in terms of negative powers of the integers o\,.. .,an. Estimates of the remainder term in the expansion are also given. Introduction. Let w be a function with integrable pth power ...

The Asymptotic Expansions for the Qdd Periodic Mathieu Functions