A ug 2 00 4 Convergence acceleration of series through a variational approach March 2 , 2008 Paolo
نویسنده
چکیده
By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Rie-mann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar exponentially convergent series for a large class of mathematical functions.
منابع مشابه
A ug 2 00 5 Convergence acceleration of series through a variational approach ⋆
By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar e...
متن کاملConvergence acceleration of series through a variational approach ⋆ Paolo
By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar e...
متن کاملConvergence acceleration of series through a variational approach February 11 , 2008
By means of a variational approach we find new series representations both for well known mathematical constants, such as π and the Catalan constant, and for mathematical functions, such as the Rie-mann zeta function. The series that we have found are all exponentially convergent and provide quite useful analytical approximations. With limited effort our method can be applied to obtain similar ...
متن کاملun 2 00 4 Markov ’ s Transformation of Series and the WZ Method
In a well forgotten memoir of 1890, Andrei Markov devised a convergence acceleration technique based on a series transformation which is very similar to what is now known as the WilfZeilberger (WZ) method. We review Markov’s work, put it in the context of modern computeraided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.
متن کامل3 1 M ay 2 00 4 Markov ’ s Transformation of Series and the WZ Method
In a well forgotten memoir of 1890, Andrei Markov devised a convergence acceleration technique based on a series transformation which is very similar to what is now known as the WilfZeilberger (WZ) method. We review Markov’s work, put it in the context of modern computeraided WZ machinery, and speculate about possible reasons of the memoir being shelved for so long.
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تاریخ انتشار 2008