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FISKE AND CHARLES S. PEIRCE 43 member of the New York Mathematical Society where he presented a number of papers, two of which were published in the American Journal of Mathematics. Although soon gaining fame as one of America's leading electrical engineers, he remained a member until his death on October 26, 1923. The other addition to the Society in 1891 is of particular interest to us. "Charles S. Peirce, B. , member of the National Academy of Sciences" was elected at the November meeting. It is of interest to learn that Van Amringe had proposed Peirce's name for membership and that Harold Jacoby had sent the invitation.

SYLVESTER, JOHNS HOPKINS AND PARTITIONS 35 We shall also require some related polynomials i-j D(i;a;q) = ai qj 2 . 0<2i*
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*Also the fishhook method was applied [2; p. 136] to give a combinatorial proof of an identity of N. J. Fine. 6. COMBINATORICS OF JACOBI'S TRIPLE PRODUCT IDENTITY One of the most important identities in the theory of elliptic theta functions is Jacobi's Triple Product Identity [7; p. 2) that W(z) = E00 zmAm, where Am = gmAm-1. J. J. SYLVESTER, JOHNS HOPKINS AND PARTITIONS 31 Consequently by iteration (z) = A0 O(z) 00 zmq(m+l/2). E m=-00 The Exodion of [28] (partly due to A. S. Hathaway) provides a very nice means of seeing that A0 is just H,,, I (I- q')'. *