History of Continued Fractions and Padé Approximants

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The book delves into the extensive history of continued fractions, tracing their origins back to Euclid's algorithm. It highlights their long-standing use prior to formal recognition and emphasizes their significance in various mathematical developments, including the proof of the transcendence of e in 1882. Continued fractions and Pade approximants are shown to be pivotal in modern spectral theory and have applications across pure and applied mathematics, numerical analysis, number theory, computer science, and more.