27 citations · 46 across the 7 of their papers we have counts for
9 papers
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.
On the Archimedean or Semiregular Polyhedra
Mark B. Villarino
We prove that there are thirteen Archimedean/semiregular polyhedra by using Euler's polyhedral formula.
Mertens' Proof of Mertens' Theorem
Mark B. Villarino
We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it…
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…