Sources in the development of mathematics : infinite series and products from the fifteenth to the twenty-first century / Ranjan Roy.
"The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli,...
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| Language: | English |
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New York :
Cambridge University Press,
2011.
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| Subjects: | |
| Physical Description: | xix, 974 pages : illustrations ; 27 cm |
| Format: | Book |
Contents:
- Machine generated contents note: 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.