scholarly journals Finite exponential series and Newman polynomials

1992 ◽  
Vol 116 (2) ◽  
pp. 313-313
Author(s):  
Bart Goddard
Keyword(s):  
Exponential Series ◽  
Newman Polynomials

scholarly journals On The Tails of the Exponential Series

1994 ◽  
Vol 37 (2) ◽  
pp. 278-286 ◽  
Author(s):  
C. Yalçin Yildirim
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Partial Sums ◽  
Maclaurin Series ◽  
Exponential Series ◽  
Asymptotic Estimation ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

AbstractA relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for ez is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of ez are also provided.

Large Newman polynomials

1986 ◽  
pp. 159-170
Author(s):  
David W. Boyd
Keyword(s):  
Newman Polynomials

scholarly journals An Iterative Method of General Planetary Theory

1974 ◽  
Vol 62 ◽  
pp. 139-155
Author(s):  
V. A. Brumberg
Keyword(s):  
Power Series ◽  
Equations Of Motion ◽  
Slight Modification ◽  
Planetary Motion ◽  
Planetary Theory ◽  
Exponential Series ◽  
Numerical Series ◽  
Satellites Of Jupiter ◽  
General Planetary Theory ◽  
The Right

This paper deals with an iterative version of the general planetary theory. Just as in Airy's Lunar method the series in powers of planetary masses are replaced here by the iterations to achieve improved approximations for the coefficients of planetary inequalities. The right-hand members of the equations of motion are calculated in closed formulas, and no expansion in powers of small corrections to the planetary coordinates is needed. For the N-planet case this method requires the performance of the analytical operations on a computer with power series of 4N polynomial variables, the coefficients being the exponential series of N-1 angular arguments. To obtain numerical series of planetary motion one has to solve the secular system using Birkhoff's normalization or the Taylor series in powers of time. A slight modification of the method in the resonant case makes it valid for the treatment of the main problem of the Galilean satellites of Jupiter.

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