Etymology

Named after Swiss mathematician Leonhard Euler (1707–1783)Category:English eponyms#EULERSCONTINUEDFRACTIONFORMULA.

Proper noun

English Wikipedia has an article on:

Euler's continued fraction formula

Wikipedia

Euler's continued fraction formulaCategory:English lemmas#EULERSCONTINUEDFRACTIONFORMULACategory:English proper nouns#EULERSCONTINUEDFRACTIONFORMULACategory:English uncountable nouns#EULERSCONTINUEDFRACTIONFORMULACategory:English multiword terms#EULERSCONTINUEDFRACTIONFORMULACategory:English entries with incorrect language header#EULERSCONTINUEDFRACTIONFORMULACategory:Pages with entries#EULER'S%20CONTINUED%20FRACTION%20FORMULACategory:Pages with 1 entry#EULER'S%20CONTINUED%20FRACTION%20FORMULA

1. (mathematicsCategory:en:Mathematics#EULERSCONTINUEDFRACTIONFORMULA) A formula connecting a finite sum of products to a finite continued fraction: ${\displaystyle a_{0}+a_{0}a_{1}+a_{0}a_{1}a_{2}+\cdots +a_{0}a_{1}a_{2}\cdots a_{n}={\cfrac {a_{0}}{1-{\cfrac {a_{1}}{1+a_{1}-{\cfrac {a_{2}}{1+a_{2}-{\cfrac {\ddots }{\ddots {\cfrac {a_{n-1}}{1+a_{n-1}-{\cfrac {a_{n}}{1+a_{n}}}}}}}}}}}}}\,.}$