From recursions to asymptotics: on Szekeres' formula for the number of partitions

@article{Canfield1997FromRT,
  title={From recursions to asymptotics: on Szekeres' formula for the number of partitions},
  author={E. Rodney Canfield},
  journal={Electr. J. Comb.},
  year={1997},
  volume={4}
}
We give a new proof of Szekeres’ formula for P (n, k), the number of partitions of the integer n having k or fewer positive parts. Our proof is based on the recursion satisfied by P (n, k) and Taylor’s formula. We make no use of the Cauchy integral formula or any complex variables. The derivation is presented as a step-by-step procedure, to facilitate its application in other situations. As corollaries we obtain the main term of the Hardy-Ramanujan formulas for p(n) = the number of unrestricted… CONTINUE READING

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