Automatic computing methods for special functions

Numerical methods for special functions

Computing Special Values of Partial Zeta Functions

We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the Eisenstein cocycle Ψ , a group cocycle for GLn(Z); the special values are computed as periods of Ψ , and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for cubic and quartic fields of small discriminant.

Computing Special Values of Motivic L-Functions

We present an algorithm to compute values L(s) and derivatives L(s) of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Γ-factor is of the form A ∏d i=1 Γ( s+λj 2 ) with d arbitrary and complex λj , not necessarily distinct. The algorithm relies on the known (or conjectural) functional equation for L(s).

islanding detection methods for microgrids

امروزه استفاده از منابع انرژی پراکنده کاربرد وسیعی یافته است . اگر چه این منابع بسیاری از مشکلات شبکه را حل می کنند اما زیاد شدن آنها مسائل فراوانی برای سیستم قدرت به همراه دارد . استفاده از میکروشبکه راه حلی است که علاوه بر استفاده از مزایای منابع انرژی پراکنده برخی از مشکلات ایجاد شده توسط آنها را نیز منتفی می کند . همچنین میکروشبکه ها کیفیت برق و قابلیت اطمینان تامین انرژی مشترکان را افزایش ...

Automatic Proof Procedures for Polynomials and Special Functions

The key prior items of work are the MetiTarski theorem prover (Cambridge) and the RAHD decision procedure (Edinburgh). RAHD1 is a proof procedure for polynomials over the reals, and MetiTarski additionally is tailored for handling special functions such as log, exp, sin and cos. Both systems are well beyond the first prototype stage, and both have already shown world-leading characteristics [1,...