Watson, G. N. Theorems stated by Ramanujan. VII: Theorems on continued fractions. (English) JFM 55.0273.01 J. Lond. Math. Soc. 4, 39-48 (1929). Verf. behandelt folgende mit gewissen unendlichen Produkten und den Eigenschaften gewisser Modulfunktionen zusammenhängende Sätze:(1) Mit \[ u = \dfrac x{1+\lower1.7ex\hbox{\(\dfrac{x^5}{1}\)}} \lower4.5ex\hbox{\({}+{}\)} \lower6.2ex\hbox{\(\dfrac{x^{10}}{1}\)} \lower7.8ex\hbox{\({}+{}\)} \lower9.5ex\hbox{\(\dfrac{x^{15}}{1}\)} \lower11.1ex\hbox{\({}+{}\)} \lower12.8ex\hbox{\(\dfrac{x^{20}}{1}\)} \lower14.3ex\hbox{\({}+\cdots\)} \] und \[ v = \dfrac{x^{\frac15}}{1} \lower1.5ex\hbox{\({}+{}\)} \lower3.0ex\hbox{\(\dfrac{x}{1}\)} \lower4.5ex\hbox{\({}+{}\)} \lower6.2ex\hbox{\(\dfrac{x^{2}}{1}\)} \lower7.8ex\hbox{\({}+{}\)} \lower9.5ex\hbox{\(\dfrac{x^{3}}{1}\)} \lower11.1ex\hbox{\({}+{}\)} \lower12.8ex\hbox{\(\dfrac{x^{4}}{1}\)} \lower14.3ex\hbox{\({}+\cdots\)} \] ist \[ v^5=u\cdot\frac{1-2u+4u^2-3u^3+u^4}{1+3u+4u^2+2u^2+u^4}. \](2) \( \dfrac{1}{1} \lower1.5ex\hbox{}{}+{}\) Reviewer: Müller, Studienassessor K. (Fürstenwalde) Cited in 1 ReviewCited in 56 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics 11A55 Continued fractions 11F03 Modular and automorphic functions JFM Section:Erster Halbband. Vierter Abschnitt. Analysis. Kapitel 11. Differenzenrechnung. Analytische Theorie der Kettenbrüche. PDFBibTeX XMLCite \textit{G. N. Watson}, J. Lond. Math. Soc. 4, 39--48 (1929; JFM 55.0273.01) Full Text: DOI