On the continued fractions of Wallis
This paper is connected with E123. Euler looks at functions f that satisfy a relation like f(x)∙f(x+1) = (b+ax)2+c, for x=0, 1, 2, .... This gives rise to a complicated improper integral that has cos(b log x) as part of its integrand.
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 5, pp. 24-44.
Opera Omnia Citation
Series 1, Volume 16B, pp.178-199.