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A simple proof of Euler's continued fraction of e1/M
| Content Provider | Scilit |
|---|---|
| Author | Tonien, Joseph |
| Copyright Year | 2016 |
| Description | A continued fraction is an expression of the form and we will denote it by the notation $[f_{0}$, $(g_{0}$, $f_{1}$), $(g_{1}$, $f_{2}$), $(g_{2}$, $f_{3}$), … ]. If the numerators $g_{i}$ are all equal to 1 then we will use a shorter notation $[f_{0}$, $f_{1}$, $f_{2}$, $f_{3}$, … ]. A simple continued fraction is a continued fraction with all the $g_{i}$ coefficients equal to 1 and with all the $f_{i}$ coefficients positive integers except perhaps $f_{0}$.The finite continued fraction $[f_{0}$, $(g_{0}$, $f_{1}$), $(g_{1}$, $f_{2}$),…, $(g_{k}$–1, $f_{k}$)] is called the k th convergent of the infinite continued fraction $[f_{0}$, $(g_{0}$, $f_{1}$), $(g_{1}$, $f_{2}$),…]. We define if this limit exists and in this case we say that the infinite continued fraction converges. |
| Related Links | https://ro.uow.edu.au/cgi/viewcontent.cgi?article=6677&context=eispapers https://www.cambridge.org/core/services/aop-cambridge-core/content/view/13F06F0985DC789AB8CC3A785D2685F1/S0025557216000656a.pdf/div-class-title-a-simple-proof-of-euler-s-continued-fraction-of-span-class-italic-e-span-span-class-sup-1-span-class-italic-m-span-span-div.pdf |
| Ending Page | 287 |
| Page Count | 9 |
| Starting Page | 279 |
| ISSN | 00255572 |
| e-ISSN | 20566328 |
| DOI | 10.1017/mag.2016.65 |
| Journal | The Mathematical Gazette |
| Issue Number | 548 |
| Volume Number | 100 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2016-07-01 |
| Access Restriction | Open |
| Subject Keyword | The Mathematical Gazette Continued Fraction |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
