Elementary Results

Bruce C. Berndt
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Bruce C. Berndt: University of Illinois at Urbana-Champaign, Department of Mathematics

Chapter Chapter 22 in Ramanujan’s Notebooks, 1994, pp 7-50 from Springer

Abstract: Abstract In this chapter we will examine Ramanujan’s findings that require only elementary high-school algebra for an understanding. A few of the results, e.g., Entries 5 and 32, however, require some knowledge of calculus for the proofs. Chapter 23, which examines Ramanujan’s discoveries in number theory, with the exception of his work on prime numbers, also contains some theorems that are accessible to those with only a background in elementary algebra. The latter results primarily involve equal sums of powers, and so it seems appropriate to place them in a chapter on number theory rather than in the present chapter. Possibly a few results in Chapter 22 fit better in Chapter 31 on elementary analysis, and possibly some would move a few results from that chapter to this chapter. Thus, the choice of material for this chapter is admittedly somewhat arbitrary.

Keywords: Elementary Result; Cube Root; Algebraic Integer; Elementary Algebra; Quartic Equation (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-1-4612-0879-2_2

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