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- W2758778865 abstract "In this paper, we investigate certain asymptotic series used by Hirschhorn to prove an asymptotic expansion of Ramanujan for the nth harmonic number. We give a general form of these series with a recursive formula for its coefficients. By using the result obtained, we present a formula for determining the coefficients of Ramanujans asymptotic expansion for the nth harmonic number. We also give a recurrence relation for determining the coefficients aj(r) such that Hn:=k=1n1k12ln(2m)++112m(j=0aj(r)mj)1/ras n, where m=n(n+1)/2 is the nth triangular number and is the EulerMascheroni constant. In particular, for r=1, we obtain Ramanujans expansion for the harmonic number." @default.
- W2758778865 created "2017-10-06" @default.
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- W2758778865 date "2018-01-01" @default.
- W2758778865 modified "2023-10-02" @default.
- W2758778865 title "Ramanujan’s formula for the harmonic number" @default.
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- W2758778865 doi "https://doi.org/10.1016/j.amc.2017.08.053" @default.
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