caa a22 4500 463178017 CHVBK 20180406164831.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s11139-007-9048-2 doi (NATIONALLICENCE)springer-10.1007/s11139-007-9048-2 Ramanujan and extensions and contractions ofcontinued fractions [Elektronische Daten] [J. Mc Laughlin, Nancy Wyshinski] If a continued fraction K n=1 ∞ a n /b n is known to converge but its limit is not easy to determine, it may be easier to use an extension of K n=1 ∞ a n /b n to find the limit. By an extension of K n=1 ∞ a n /b n we mean a continued fraction K n=1 ∞ c n /d n whose odd or even part is K n=1 ∞ a n /b n . One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the odd part, if K n=1 ∞ a n /b n is the even part); (iii) Find the limit of the other contraction and show that the odd and even parts of the extension tend to the same limit. We apply these ideas to derive new proofs of certain continued fraction identities of Ramanujan and to prove a generalization of an identity involving the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith and Brillhart. Springer Science+Business Media, LLC, 2007 Continued fractions nationallicence Convergence nationallicence Extension nationallicence Mc Laughlin J. Mathematics Department, Trinity College, 300 Summit Street, 06106-3100, Hartford, CT, USA aut Wyshinski Nancy Mathematics Department, Trinity College, 300 Summit Street, 06106-3100, Hartford, CT, USA aut The Ramanujan Journal Springer US; http://www.springer-ny.com 14/3(2007-12-01), 389-404 1382-4090 14:3<389 2007 14 11139 https://doi.org/10.1007/s11139-007-9048-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11139-007-9048-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mc Laughlin J. Mathematics Department, Trinity College, 300 Summit Street, 06106-3100, Hartford, CT, USA aut NATIONALLICENCE 700 1- Wyshinski Nancy Mathematics Department, Trinity College, 300 Summit Street, 06106-3100, Hartford, CT, USA aut NATIONALLICENCE 773 0- The Ramanujan Journal Springer US; http://www.springer-ny.com 14/3(2007-12-01), 389-404 1382-4090 14:3<389 2007 14 11139 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer