Elementary Analysis on Ramanujan's Nested Radicals

Ramanujan’s work on nested radicals produced identities that look impossible until you see the proofs. This book covers the full theory, from basic denesting to Ramanujan’s most general formulas.

The fundamentals section covers definitions, notation, and denesting techniques. Ramanujan’s general formula is derived from the binomial theorem.

Convergence theory is handled rigorously via Herschfeld’s theorem. The connection between nested radicals and continued fractions is explored in depth.

The book includes Ramanujan’s ultimate nested radical formula, his “wild theorem,” and the calculus of nested radicals.

Key Topics

• Denesting techniques for nested radicals
• Ramanujan’s general formula from the binomial theorem
• The golden ratio and plastic constant as nested radical limits
• Herschfeld’s convergence theorem
• Connection to continued fractions
• Calculus of functions defined by nested radicals