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Abstract. The continued fraction expansions of a certain class of numbers of the form u-k0 + u -k, + u-k2 + ...have a definite pattern.Recently J. SHALLIT [1] has shown that the simple continued fractions for the rational numbers B(u,v) =u -~ +u-2+u-4+ ... +u -2" and for the transcendental numbers o0

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We discuss various methods to compute the Fourier coefficients of the elliptic modular function j(z). We present run times to compute the coefficients in practice. If possible, we discuss the theoretical complexity of the corresponding method, too. We conclude that, in practice, an approach due to Kaneko and Zagier turns out to be most efficient.

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