On $L_p$ Chebyshev-Cramer Asymptotic Expansions

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...

Optimizing Spectral Sums using Randomized Chebyshev Expansions

The trace of matrix functions, often called spectral sums, e.g., rank, log-determinant and nuclear norm, appear in many machine learning tasks. However, optimizing or computing such (parameterized) spectral sums typically involves the matrix decomposition at the cost cubic in the matrix dimension, which is expensive for large-scale applications. Several recent works were proposed to approximate...

On the Coefficients in Asymptotic Factorial Expansions

Here p and q are non-negative integers with pûq\ the a i and p¡ denote arbitrary complex parameters and w denotes a complex variable. It is known from a lemma which appears in the work of W. B. Ford [l ], E. M. Wright [5], and H. K. Hughes [2] that Pgq(w) admits an asymptotic factorial expansion in every right half-plane. Moreover, it follows from their investigations that the coefficients occu...

Asymptotic Expansions Methodsand Applications

Feynman diagrams are the most important theoretical tool for particle physicists. They are an efficient link between theory and experiment. However, their translation into actual numerical predictions is often very tedious if not impossible. Huge efforts have been devoted to their evaluation, and several powerful methods have been developed to systemize their treatment. The more complex a Feynm...

Asymptotic Expansions for Integrals