stieltjes series
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2009 ◽  
pp. 193-275
Author(s):  
George A. Baker ◽  
Peter Graves-Morris
Keyword(s):  

2009 ◽  
Vol 32 (2) ◽  
pp. 231-237
Author(s):  
Saroj Kumar Dash ◽  
Tanaya Patel ◽  
Swadheenananda Pattanayak
Keyword(s):  
The Mean ◽  

Author(s):  
Jens Marklof ◽  
Yves Tourigny ◽  
Lech Wołowski

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.


2004 ◽  
Vol 30 (2) ◽  
pp. 123-136 ◽  
Author(s):  
Ferenc Móricz
Keyword(s):  

2002 ◽  
Vol 78 (1) ◽  
pp. 51-57
Author(s):  
F. Móricz
Keyword(s):  

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