Cambridge University Press 978-0-521-11470-7 - Sources in the Development of Mathematics: Infinite Series and Products from the Fifteenth to the Twenty-first Century Ranjan Roy Index More information Index Abel, Niels Henrik, 57, 58, 60, 61, 63–65, 67, 69, 70, Andrews, George, 345, 475, 608, 626, 634, 637, 643, 91, 182, 195, 291, 292, 302, 305–307, 310, 316, 650, 651, 678, 679 317, 325, 371, 417, 447, 461, 499, 503, 508, 509, Andrews, George, 548 514, 519, 602, 691, 692, 703, 704, 750–753, 755, Angeli, Stephano degli, 99, 264 777, 780, 801, 803–805, 816–827, 829–832, 837, Apollonius, 71 844, 852, 856, 863–866, 887, 891 Appell, Paul, 405, 890 Abhyankar, Shreeram, 146, 729 approximate quadrature, 11, 161, 168, 175, 225, absolutely convergent Fourier series, 759, 772, 773 578, 582 Academia Algebrae, 19, 26 Arbogast, Louis, 368–370, 374–376, 379, 385, 391, Acosta, D. J., 96 398, 663 Acta Eruditorum, 122, 126, 197, 219, 240, 243, Archimedean spiral, 78 271, 605 Archimedes, 6, 16, 25, 99 Adams, John Couch, 629 Archimedes’s formula, 6, 13, 16 addition formula for elliptic functions, 803, 804, 817, area inequalities, 910, 911, 914 839, 865 arithmetic-geometric mean, 794, 798, 799, 801, 809, addition formula for elliptic integrals, 781, 814 810, 814–816 Aepinus, Franz, 59 Arithmetica Infinitorum, 28, 29, 50, 52, 120, 148, 446 Ahlfors, Lars, 553, 892, 912, 928 Arithmetica Logarithmica, 159 Ahlgren, Scott, 635, 652 Arithmetica Universalis, 83, 94, 96, 328 Aiyar, T. V. V., 14 Arithmeticorum Libri Duo, 17 Akhiezer, N. I., 590, 597 Arnold, Vladimir, 119, 754, 777 Aronhold, Siegfried, 725, 726, 747 Alder, H. L., 632, 652 Ars Conjectandi, 18, 19, 26, 347, 605 d’Alembert, Jean, 56, 203, 212, 214, 215, 221, 246, Artin, Emil, 450, 462–464, 471, 475, 931 254, 267, 313, 348, 354, 355, 365, 369, 370, 401, Artis Analyticae Praxis, 82 402, 410, 426 Artis Magnae, 311 Alexander, J. W., 910, 927 Artmann, B., 535 algebraic analysis, 69, 205, 290, 367, 373 Aryabhatyabhasya, 2, 3, 867 algebraically independent numbers, 876, 877, 885 Ash, J. Marshall, 443 Almagest, 13, 158 Ashworth, Margaret, 635 Almkvist, Gert, 814 Askey, Richard, 390, 473, 475, 548, 597, 619, 659, Altmann, Simon, 597, 626 676, 679, 926–928 Analyse algébrique, 56, 67–69, 154, 166, 175, 221, Askey–Gasper inequality, 926 295, 308, 775 Atkin, A. O. L., 634, 635, 650, 652 analytic continuation, 753, 801 Aubrey, John, 31 analytical engine, 729 Analytical Society, 291, 370, 398 Anderson, Alexander, 151 Babbage, Charles, 368, 370, 371, 380, 398, 399, 729 Anderson, Marlow, 15, 719 Bäcklund, R.J., 895, 896, 898, 906 959 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-11470-7 - Sources in the Development of Mathematics: Infinite Series and Products from the Fifteenth to the Twenty-first Century Ranjan Roy Index More information 960 Index Baernstein, Albert, 927, 928 beta integral, 41, 42, 101, 119, 222, 233, 234, 237, Bag, Amulya Kumar, 12, 15 324, 349, 453, 460, 461, 473, 475, 551, 589, 600, Bailey, D., 546 655, 784 Bailey, W. N., 678, 679 multidimensional, 473, 475 Baillaud, B., 49 Betti, Enrico, 837 Baker, Alan, 877, 885, 886 Beukers, Frits, 876, 886 Baker, H. F., 649 Bézout, Étienne, 313, 374, 727, 728 Banach, Stefan, 773 Bhaskara, 4, 9, 10, 13, 36, 681 Bieberbach, Ludwig, 907, 910, 911, 916, 917, 919, Banach algebras, 759, 773, 774 921–923, 928 Barnes, E. W., 473, 553, 554, 649 Bieberbach conjecture, 907, 910–913, 916, 917, 922, Barnes’s integral, 473, 554 923, 926, 928 Baron, Margaret, 119 Binet, Jacques, 480, 486–491, 493 Barrow, Isaac, 97–100, 104, 106–115, 118, 119, 121, Binet’s integral formulas, 480, 486, 490 141, 147, 156, 238, 260, 261 binomial coefficients, 21, 53, 159, 556, 611 Bartels, Johann, 801, 802 additive rule, 51 Basarab–Horwath, P., 906 multiplicative rule, 51 Bateman, Harry, 199, 220 binomial theorem, 12, 51, 52, 54–58, 60–62, 65, 66, Bateman, P. T., 719 68–70, 101, 140, 142, 147, 148, 154, 159, 176, Baxter, R. J., 658 184, 203, 210, 248, 249, 289, 292, 293, 372, 374, Bazilevich, I. E., 913 384, 386, 604, 618, 661, 779, 799, 801, 932, de Beaune, Florimond, 127, 138, 202, 210, 260, 344 938, 941 Beery, Janet, 175 non-commutative, 383 Bell, Eric Temple, 723 biquadratic reciprocity, 854 Berggren, Lennart, 814 al-Biruni, 158 Berkeley, George, 80 Bissell, Christopher, 79 Berndt, Bruce, 571, 625, 652, 814, 866 Blanton, J. D., 199 Bloch, André, 892 Bernoulli, Daniel, 18, 180, 232, 246, 252–254, 259, Boas, Ralph, 905 262, 263, 265, 266, 285, 286, 288, 290, 401–403, 426, 445, 474, 494, 499, 507, 517, 577, 781, 868, Bodenhausen, Rudolf von, 123, 129, 139 869, 886 Boehle, K., 872 Bohr, Harald, 33, 37, 81, 444, 450, 462–464, 475, 754 Bernoulli, Jakob, 18–26, 97, 122, 178, 190, 193, 197, Bohr, Niels, 756 210, 227, 262, 264, 265, 271, 278, 287, 330, 477, Boilly, Julien, 817 481, 495, 497, 505, 515, 516, 601, 602, 605, 623, du Bois-Reymond, Paul, 440 625, 778, 779, 784, 786, 787 Bolibruch, A. A., 886 Bernoulli, Johann, 18, 19, 38, 122, 123, 131–133, Bollobás, B., 906 136–139, 152, 157, 178, 202, 210–212, 219–222, Bolyai, János, 806 224, 226, 227, 238, 240, 243, 261–264, 271–273, Bolyai, Wolfgang, 806 287, 289, 291, 304, 330, 346, 347, 367, 368, 373, Bolza, Oskar, 366 385, 403, 445, 447, 453, 515, 523, 525–527, 570, Bolzano, Bernard, 56, 204–206, 218, 219, 348, 440 628, 778, 779, 781 Bombelli, Rafael, 33, 34 Bernoulli, Johann II, 18 Bombieri, Enrico, 906 Bernoulli, Niklaus, 19 Bond, Henry, 104 Bernoulli, Niklaus I, 18, 19, 179, 186, 245, 246, 253, Bonnet, Pierre Ossian, 205 265, 290, 298–300, 310, 330, 346, 347, 366, 477, Book on Polygonal Numbers, 17 517, 527, 528, 545 Boole, George, 283, 284, 287, 369, 371–373, Bernoulli, Niklaus II, 18, 265, 445 387–390, 398, 399, 512, 663, 720–723, 727, Bernoulli numbers, 18, 22–24, 26, 304, 337, 479, 485, 729–733, 746, 747 494, 495, 499, 505, 509, 511, 513, 518, 519, 522, Boole summation formula, 512 523, 544, 774 Borchardt, Carl, 820, 858, 859 Bernoulli polynomials, 20, 23, 24, 403, 494, 498, 499, Borel, Émile, 362, 658, 775, 890–892, 898, 900, 505, 507, 508, 517 902–904, 908, 909 Bers, Lipman, 928 Boros, George, 243, 244 Bertrand, Joseph, 348, 697, 705, 708, 717 Borwein, Jonathan, 546, 814 Bertrand’s conjecture, 697, 705, 707, 717 Borwein, Peter, 814 Bessel, F. Wilhelm, 160, 286, 361, 450, 452, 453, 480, Bos, Henk, 139 550, 573, 696, 719, 801, 874–876 Bose, S. N., 284 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-11470-7 - Sources in the Development of Mathematics: Infinite Series and Products from the Fifteenth to the Twenty-first Century Ranjan Roy Index More information Index 961 Bottazzini, Umberto, 259, 288, 426 Cartan, Élie, 350 Bouquet, Jean Claude, 268, 820 Cartan, Henri, 350, 351, 900, 906 Bourbaki, Nicolas, 33, 50, 139, 350, 351, 365, 911 Cartier, Pierre, 392 Bourget, H., 49 Cartwright, Mary L., 754 Boutroux, Pierre, 909 Casorati, Felice, 14, 891 Boyer, Carl, 13, 25 Casorati–Weierstrass theorem, 891, 906 Boylan, Matthew, 635 Castillione, Johan, 156 brachistochrone, 132, 133, 138, 139, 347, 351 Catalan, Eugène, 751 Bradley, Robert E., 69, 398, 775 Cataldi, Pietro Antonio, 33, 34 Brahmagupta, 13, 158, 681 catenary, 122, 123, 129–131, 139, 269 de Branges, Louis, 907, 910, 912, 914, 923–926, 928 Cauchy, Augustin–Louis, 56, 57, 60–64, 67–69, 85, Brashman, N. D., 590 86, 89, 96, 152, 154, 161, 163, 166, 167, 174, Bressoud, David, 15, 27, 221, 443, 573, 632 175, 203–206, 213, 216–221, 268, 290, 295–298, Briggs, Henry, 18, 51, 53, 159, 160 308, 329, 335–338, 345, 346, 348–350, 352–354, Bringmann, Kathrin, 637 361, 365, 369, 371, 417, 418, 427, 430, 441, 449, Brinkley, John, 378, 379, 399 461, 462, 467, 479, 480, 488, 489, 491, 498, 501, Brioschi, Francesco, 837 509, 519, 538, 551, 553, 586, 604, 618, 621, 625, Briot, C., 268, 820 653, 720, 751, 775, 813, 819–821, 849–851, 872, Brisson, Barnabé, 368 888, 898, 909, 918, 919, 921 Bromhead, Edward, 350, 370 Cauchy product, 61, 63, 67, 751, 752 Bronstein, Manuel, 228, 244 Cauchy’s integral formula, 361, 873, 895, 896 Bronwin, Brice, 162, 171, 172 Cavalieri, Bonaventura, 29, 99, 168 Brouncker, William, 14, 31–34, 38, 40, 43, 50, 141, Cayley, Arthur, 284, 371, 373, 395–397, 577, 606, 681, 868 608, 617, 629, 642–645, 652, 663, 720–726, 728, Brownwell, W. D., 876 729, 732–740, 742, 743, 745, 747, 748, 791, 792, Brun, Viggo, 69 795, 814, 880 Buchan, John, 637 Cesàro, Ernesto, 751, 752, 754, 776 Buchler, Justus, 630 Chabert, Jean–Luc, 175 Budan, François, 93, 94 Chandrasekhar, S., 99, 119 Bullialdus, Ismael, 22 Charzynski, Z., 912 Bunyakovski, Viktor, 86, 697 Chebyshev, Pafnuty, 50, 162, 163, 172–175, 578, Burckel, Robert, 573 590–598, 692, 697, 698, 700–712, 714, 715, Burn, R. P., 288 717, 719 Burns, Robert, 719 Chen Jing–Run, 927 Burnside, William, 649 Cheney, E. W., 679 Burnside, William Snow, 94 Chern, S. S., 892 Byron, Lord George Gordon, 729 Cherry, William, 906 Child, J. M., 79, 114–119 Chowla, Sarvadaman, 633 Cahen, Eugène, 554, 700, 718, 776 Christoffel, Elwin B., 908 Cambridge and Dublin Mathematical Journal, Chu, Shih–Chieh (also Zhu Shijie), 184, 199, 601, 369, 372 619, 728 Cambridge Mathematical Journal, 372 Chu–Vandermonde identity, 154, 620 Campbell, George, 84, 92, 96 q-extension, 620, 653 Campbell, Paul J., 287 Chudnovsky, D.