By Richard Askey, Uta C. Merzbach

ISBN-10: 0821801244

ISBN-13: 9780821801246

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Then these curves will 48 CAROLYN EISELE represent the meridians and parallels of a new projection having north poles and south poles wherever the component projections had such poles. Functions may, of course, be classified according to the pattern of the projection produced by such a transformation of the stereographic projection with a pole at the tangent points. Thus we shall have1. Functions with a finite number of zeros and infinities (algebraic functions). 2. Striped functions (trigonometric functions).

M. V. 4) by noting further invariants in Franklin's transformation, and these observations have been extended to other identities [5]. Finally [9] Ferrers graphs can be analyzed by putting in J. J. SYLVESTER, JOHNS HOPKINS AND PARTITIONS 27 successive Durfee squares underneath each other. For example, the Ferrers graph of 5+5+4+4+4+3+3+2+ 1 + 1 is with five successive Durfee squares. Successive Durfee squares enter into one extension of the Rogers-Ramanujan identities [9]. THEOREM. The number of partitions of n with at most k successive Durfee squares equals the number of partitions of n into parts not congruent to 0, ±k (mod 2k + 1).

The first ten volumes of the AJM contained papers by about ninety different writers and covered the years 1878 to 1888. About thirty were mathematicians of foreign countries; another twenty were pupils of Professor Sylvester; 41 42 CAROLYN EISELE others had come under the influence of Benjamin Peirce; some had been students at German Universities; some were in large degree self-trained. Several of them had already sent papers abroad for publication in foreign journals. Among the contributors to the early volumes of the American Journal of Mathematics special mention must be made of Newcomb, Hill, Gibbs, C.

### A Century of mathematics in America (History of Mathematics, Vol 1) by Richard Askey, Uta C. Merzbach

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