Two-point Padé approximants for formal Stieltjes series

1994 ◽  
Vol 8 (2) ◽  
pp. 313-328 ◽  
Author(s):  
Stanisław Tokarzewski ◽  
Jerzy Bławzdziewicz ◽  
Igor Andrianov
Keyword(s):  
Padé Approximants ◽  
Pade Approximants ◽  
Stieltjes Series

Padé approximants of random Stieltjes series

2007 ◽  
Vol 463 (2087) ◽  
pp. 2813-2832
Author(s):  
Jens Marklof ◽  
Yves Tourigny ◽  
Lech Wołowski
Keyword(s):  
Continued Fraction ◽  
Bessel Functions ◽  
Padé Approximants ◽  
Independent Random Variables ◽  
Disordered System ◽  
One Dimensional ◽  
Pade Approximants ◽  
Explicit Formulae ◽  
Stieltjes Series ◽  
Positive Half

We consider the random continued fraction where s n are independent random variables with the same gamma distribution. Every realization of the sequence defines a Stieltjes function that can be expressed as for some measure σ on the positive half-line. We study the convergence of the finite truncations of the continued fraction or, equivalently, of the diagonal Padé approximants of the function S . Using the Dyson–Schmidt method for an equivalent one-dimensional disordered system and the results of Marklof et al. , we obtain explicit formulae (in terms of modified Bessel functions) for the almost sure rate of convergence of these approximants, and for the almost sure distribution of their poles.

scholarly journals Padé approximants for the ground-state energy of closed-shell quantum dots

1997 ◽  
Vol 56 (24) ◽  
pp. 15740-15743 ◽  
Author(s):  
Augusto Gonzalez ◽  
Bart Partoens ◽  
François M. Peeters
Keyword(s):  
Quantum Dots ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Closed Shell ◽  
Padé Approximants ◽  
Pade Approximants
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