An extension of Landen transformations

There is no file associated with this item.
Disclaimer 
Access requires a license to the Dissertations and Theses (ProQuest) database. 
Link to File 
http://libproxy.tulane.edu:2048/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.882004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3210887 
Title 
An extension of Landen transformations 
Author 
Manna, Dante V 
School 
Tulane University 
Academic Field 
Mathematics 
Abstract 
A Landen transformation is a transformation on the parameters of a definite integral that fixes its value. The earliest discovery of such a transformation was the arithmeticgeometric mean iteration, phi: (a, b) ((a + b)/2, ab ). Gauss connected the limit of this iteration to the complete elliptic integral, whose value is fixed under phi. This result both links the study of integrals and Number Theory and provides a quadratically convergent numerical method for approximating an elliptic integral We present a Landen transformation for a rational integral over the real line. This generalizes the work done by Boros and Moll for the even case. Let Rp :=&cubl0;a&ar;e R2p&vbm0;I a&ar;< infinity&cubr0 ;, where a&ar;:= a0,&ldots;,ap;b0,&ldots;,b p2and Ia&ar; := RRx dx , with Rx :=BxA x=b0xp 2+&cdots;+bp2a0xp +a1xp1+&cdots;+ap. We construct, for all 2 ≤ m, p ∈ N , a rational Landen transformation Lm,p :Rp Rp , and prove its scaled version converges to a limit in R2p with convergence order m. We also prove the invariant property Ia&ar; =I&parl0;Lm,p a&ar; &parr0 ;, which leads to the formula RR xdx=pLa &d1 ;, where La&ar; :=lim n→infinitybn 0an 0, Lnm, na =:&parl0;a n0,a n1,&cdots;,a np;b n0,&cdots;b np2&parr0; is the limit of the Landen iteration. This generates a numerical method for a rational integral which converges to order m 
Language 
eng 
Advisor(s) 
Moll, Victor H 
Degree Date 
2006 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
2006 
Source 
Source: 106 p., Dissertation Abstracts International, Volume: 6703, Section: B, page: 1473 
Identifier 
See 'reference url' on the navigation bar. 
Rights 
Copyright is in accordance with U.S. Copyright law 
Contact Information 
acase@tulane.edu 
Rating 

Add tags for An extension of Landen transformations
you wish to report:
...