On Some Asymptotic Formulas in the Theory of Partitions

They also conjectured that for Jki<feâ£o, pk!(n)Spk2(n) and for ko<h<k2i pki(n)<pk2(n). They verify this conjecture for n^32. Recently Todd published a table of all the pkin) for n^lOO, and it is easy to verify the conjecture for w^glOO. I am unable to prove or disprove this conjecture. They also remark that pk0{n) differs from c-inm i0g n by i e s s than 1 for n^ 32; (2) shows that for large n the difference tends to infinity. Lehner and P proved that if we denote