Series and Products in the Development of Mathematics

Ranjan Roy is the Ralph C. Huffer Professor of Mathematics and Astronomy at Beloit College, Wisconsin, and has published papers and reviews on Riemann surfaces, differential equations, fluid mechanics, Kleinian groups, and the development of mathematics. He has received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching, and was twice named Teacher of the Year at Beloit College. He co-authored Special Functions (2001) with George Andrews and Richard Askey and co-authored chapters in the NIST Handbook of Mathematical Functions (2010); he also authored Elliptic and Modular Functions from Gauss to Dedekind to Hecke (2017) and the first edition of this book, Sources in the Development of Mathematics (2011).

Volume 1: 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. The calculus of Newton and Leibniz; 8. De Analysi per Aequationes Infinitas; 9. Finite differences: interpolation and quadrature; 10. Series transformation by finite differences; 11. The Taylor series; 12. Integration of rational functions; 13. Difference equations; 14. Differential equations; 15. Series and products for elementary functions; 16. Zeta values; 17. The gamma function; 18. The asymptotic series for ln Γ(x); 19. Fourier series; 20. The Euler–Maclaurin summation formula; 21. Operator calculus and algebraic analysis; 22. Trigonometric series after 1830; 23. The hypergeometric series; 24. Orthogonal polynomials; Bibliography; Index; Volume 2: 25. q-series; 26. Partitions; 27. q-Series and q-orthogonal polynomials; 28. Dirichlet L-series; 29. Primes in arithmetic progressions; 30. Distribution of primes: early results; 31. Invariant theory: Cayley and Sylvester; 32. Summability; 33. Elliptic functions: eighteenth century; 34. Elliptic functions: nineteenth century; 35. Irrational and transcendental numbers; 36. Value distribution theory; 37. Univalent functions; 38. Finite fields; Bibliography; Index.