27 citations · 61 across the 9 of their papers we have counts for
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Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number
Mark B. Villarino
An algebraic transformation of the DeTemple-Wang half-integer approximation to the harmonic series produces the general formula and error estimate for the Ramanujan expansion for t…
A Direct Proof of Landen's Transformation
Mark B. Villarino
We prove Landen's transformation by a direct elementary transformation of infinite series
Ramanujan's Inverse Elliptic Arc Approximation
Mark B. Villarino
We suggest a continued fraction origin to Ramanujan's approximation to {(a-b)/(a+b)}^2 in terms of the arc length of an ellipse with semiaxes a and b. Moreover, we discuss the asym…
Ramanujan's Perimeter of an Ellipse
Mark B. Villarino
We present a detailed error analysis of Ramanujan's most accurate approximation to the perimeter of an ellipse.
Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series
Mark B. Villarino
A simple integration by parts and telescopic cancellation leads to a rigorous derivation of the first 2 terms for the error in Ramanujan's asymptotic series for the nth partial sum…