Convergence acceleration of series through a variational approach |
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Authors: | Paolo Amore |
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Institution: | Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico |
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Abstract: | 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 exponentially convergent series for a large class of mathematical functions. |
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Keywords: | Acceleration of convergence Riemann zeta function Hurwitz zeta function Linear delta expansion Variational perturbation theory |
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