Priyanshu Kumar

Reconstructing and Extending Ramanujan's 1914 Series for 1/π: A Line-by-Line Proof of the Modular Equation Theory, With Five New Quartic-Theory Series

This paper has two parts. First, we give a complete, self-contained reconstruction of the proof of Equation 3 in Ramanujan's 1914 paper "Modular equations and approximations to π" [Ramanujan 1914], starting from the elementary problem of the perimeter of an ellipse and building u...

Reconstructing and Extending Ramanujan's 1914 Series for 1/π: A Line-by-Line Proof of the Modular Equation Theory, With Five New Quartic-Theory Series

This paper has two parts. First, we give a complete, self-contained reconstruction of the proof of Equation 3 in Ramanujan's 1914 paper "Modular equations and approximations to π" [Ramanujan 1914], starting from the elementary problem of the perimeter of an ellipse and building u...