English Title

Eminent properties of series within which the general term is contained as x = (1/2)(a+b/√k)(p+q√k)n + (1/2)(a-b/√k)(p-q√k)n

Authors

Leonhard Euler

Enestrom Number

453

Fuss Index

146

Original Language

Latin

Content Summary

Euler studies the nth order form fvn+gun. He derives the recursive relation f(n+2) = 2pf (n+1) − rf(n) and gets results on the numbers of the form p2kq2. Euler's work is made more difficult by the fact that he has not yet begun to use subscripts. Instead, he invents a notation [n] to denote the nth term of a sequence. Of course, he can only refer one sequence at a time with this notation, but it is a significant improvement on anything he's used before. This paper is best considered alongside the number theory papers E452 and E454.

Published as

Journal article

Published Date

1774

Written Date

1772

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 18, pp. 198-217.

Opera Omnia Citation

Series 1, Volume 15, pp.185-206.

Record Created

2018-09-25

Included in

Mathematics Commons

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