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On a Continued Fraction of Stieltjes
Published online by Cambridge University Press: 03 November 2016
Extract
1. One of the two curious self-reciprocal formulae stated by Rama-nujan,
where
of which I have recently given a proof, can be established by using a result proved by Stieltjes that, if x > 0, m ≥ 0, 0≤a≤ 1,
The proof only requires the above result in the case in which m = 1, a = 0. While seeking an extension of the result (1. 1), I have obtained an expression for the continued fraction (1. 3) in the form of an infinite series.
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- Copyright © Mathematical Association 1932
References
page no 257 note * Collected Papers, 334.
page no 257 note † Journal London Math. Soc. 4 (1929), 310-13.
page no 257 note ‡ Quart. J. of Math. 35 (1904), 195.
page no 257 note § Proc. London Math. Soc. (2), 33 (1931), 226.