Abstract
are classical, (a) being the so-called pentagonal number of Euler, and (b) being an identity of Jacobi's, well known in the theory of elliptic modular functions. It is remarkable that for no other values of r are the coefficients of HJ(1-Xn)t known explicitly. It will be the purpose of this paper to give various recursion formulas and identities for these coefficients, which are consequences of identities between functions on certain modular subgroups. In particular, the coefficients will be investigated thoroughly for r=2, 4, 6. A typical theorem is that every integer occurs as the modulus of the coefficients for r =2.
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