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Informationen zum Autor Ranjan Roy is the Ralph C. Huffer Professor of Mathematics and Astronomy at Beloit College. Roy has published papers and reviews in differential equations! fluid mechanics! Kleinian groups! and the development of mathematics. He co-authored Special Functions (2001) with George Andrews and Richard Askey! and authored chapters in the NIST Handbook of Mathematical Functions (2010). He has received the Allendoerfer prize! the Wisconsin MAA teaching award! and the MAA Haimo award for distinguished mathematics teaching. Klappentext A look at the discovery and use of infinite series and products from Wallis and Newton through Euler and Gauss to the present day. Zusammenfassung Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators! including Wallis! Newton! Euler! Gauss! Jacobi! Cayley! Sylvester and Hilbert. The text provides context and motivation for these discoveries! with many detailed proofs! offering a valuable perspective on modern mathematics. Inhaltsverzeichnis 1. Power series in fifteenth-century Kerala; 2. Sums of powers of integers; 3. Infinite product of Wallis; 4. The binomial theorem; 5. The rectification of curves; 6. Inequalities; 7. Geometric calculus; 8. The calculus of Newton and Leibniz; 9. De Analysi per Aequationes Infinitas; 10. Finite differences: interpolation and quadrature; 11. Series transformation by finite differences; 12. The Taylor series; 13. Integration of rational functions; 14. Difference equations; 15. Differential equations; 16. Series and products for elementary functions; 17. Solution of equations by radicals; 18. Symmetric functions; 19. Calculus of several variables; 20. Algebraic analysis: the calculus of operations; 21. Fourier series; 22. Trigonometric series after 1830; 23. The gamma function; 24. The asymptotic series for ln GAMMA(x); 25. The Euler-Maclaurin summation formula; 26. L-series; 27. The hypergeometric series; 28. Orthogonal polynomials; 29. q-Series; 30. Partitions; 31. q-Series and q-orthogonal polynomials; 32. Primes in arithmetic progressions; 33. Distribution of primes: early results; 34. Invariant theory: Cayley and Sylvester; 35. Summability; 36. Elliptic functions: eighteenth century; 37. Elliptic functions: nineteenth century; 38. Irrational and transcendental numbers; 39. Value distribution theory; 40. Univalent functions; 41. Finite fields. ...
