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Cambridge University Press 978-1-108-70945-3 — Series and Products in the Development of Mathematics Vol 1, 2Nd Ed Cambridge University Press 978-1-108-70945-3 — Series and Products in the Development of Mathematics Vol 1, 2nd ed. Ranjan Roy Index More Information Index Abel, Niels Henrik, 88, 90, 93, 95–99, 102–104, 137, Arithmetica Universalis, 118, 140, 142 220, 242, 253, 367, 368, 385, 387, 388, 394, 402, Ars Conjectandi, 26, 27 448, 449, 471, 543, 556, 562, 563, 569, 584, 600 Artin, Emil, 443, 486, 488, 496 Abel mean, 569, 579 Artis Analyticae Praxis, 117 Abhyankar, Shreeram, 172 Aryabhatyabhasya, 2, 3 Acosta, D. J., 142 Ash, J. Marshall, 656 Acta Eruditorum, 145, 150, 244, 271, 303, 305, 342 Askey, Richard, 458, 482, 498, 628, 659, 709, 710, Aepinus, Franz, 91 720 Ahlfors, Lars, 664 asymptotic series, 503, 506 Aiyar, T. V. V., 22 Aubrey, John, 58 Akhiezer, N. I., 712, 720 al-Biruni, 188 Babbage, Charles, 597, 599, 600, 616, 638 al-Haytham, 8, 20, 21, 24, 30, 241 Bag, Amulya Kumar, 20, 22 al-Karaji, 81 Baillaud, B., 76 al-Kashi, 81, 166 Barnes, E. W., 498, 664, 665 al-Samawal, 81 Barnes’s integral, 498, 666 d’Alembert, Jean, 87, 250, 251, 262, 265, 266, 307, 322, 337, 524–526, 536, 598, 599 Barrow, Isaac, 144, 167, 173, 301, 328, 329 algebraic analysis, 103, 254, 366, 596, 602 de Beaune, Florimond, 151, 249, 260, 328 Almagest, 21, 186 Beery, Janet, 212 Altmann, Simon, 720 Berkeley, George, 115 Analyse alg´ebrique, 88, 101–103, 181, 202, 374, 394 Berndt, Bruce, 48, 686 Analytical Society, 368, 599, 600, 638 Bernoulli, Daniel, 26, 218, 284, 307, 319–321, 327, Anderson, Alexander, 178 331, 332, 334, 335, 361–364, 366, 399, 400, 437, Anderson, G. W., 477 438, 524, 526, 527, 556, 562, 580–582, 692 Anderson, Marlow, 22 Bernoulli, Jakob, 26, 27, 31, 33–35, 37, 40, 41, 48, Andrews, George, 659 145, 146, 215, 229, 240, 245, 260, 278, 330, 333, Angeli, Stephano degli, 333 334, 341, 352, 353, 396, 398, 416, 430, 500, 507, Aomoto, K., 478 557, 560, 574, 581 Apianus, Petrus, 82 Bernoulli, Johann, 26, 27, 145, 146, 156–159, Apollonius, 105 162–164, 179, 185, 215, 249, 250, 259–262, 271, Appell, Paul, 530 273, 275–279, 301, 303, 329–333, 341–344, 365, approximate quadrature, 19, 192, 204, 276, 692, 697 367, 381, 386, 396, 405, 407–410, 437, 440, 527, Arbogast, Louis, 597–599, 603, 609, 610, 615, 621, 596, 597, 603, 622, 684 622, 629, 638 Bernoulli, Johann, II, 26 Archimedean spiral, 114 Bernoulli, Niklaus, 27 Archimedes, 23 Bernoulli, Niklaus I, 26, 27, 216, 225, 286, 306, 307, Arithmetica Infinitorum, 54, 55, 76, 83, 143, 174 320, 334, 366, 378–380, 399, 410, 411, 500 Arithmetica Logarithmica, 188 Bernoulli, Niklaus II, 26, 334, 437 750 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-108-70945-3 — Series and Products in the Development of Mathematics Vol 1, 2nd ed. Ranjan Roy Index More Information Index 751 Bernoulli numbers, 26, 35, 400, 402, 404, 405, 423, Brouncker, William, 57, 58, 61, 62, 67, 68, 72, 76, 505, 512, 557, 562, 592, 594 167, 469 recurrence relations, 34, 48 Brun, Viggo, 104 Bernoulli polynomials, 33, 35, 44, 400, 527, 562 Budan, Franc¸ois, 139, 140 Fourier series of, 429 Bullialdus, Ismael, 34 Bessel, F. Wilhelm, 198, 362, 444–446, 506, 661 Bunyakovski, Viktor, 122 beta integral, 273, 297, 465, 468, 470–472, 498, 662, Burn, R. P., 364 705 Burnside, William Snow, 140 Selberg, 476 Bezout,´ Etienne,´ 604 Cahen, Eugene,` 665 Bhaskara, 4, 10, 15, 21, 64 Cambridge and Dublin Mathematical Journal, 598, Bhattopala, 79, 80 602 Binet, Jacques, 505, 514–516, 522, 523 Cambridge Mathematical Journal, 602 Binet’s integral formulas, 505, 514, 522 Campbell, George, 119, 120, 125, 138, 142 binomial coefficients, 33, 84, 188, 668 Campbell, Paul J., 363 binomial theorem, 20, 77, 82, 85, 86, 89–91, 94–96, Cannon, John T., 363 98, 100, 102, 103, 165, 168, 173, 174, 181, 189, Cantor, Georg, 103, 253, 254, 256, 640, 641, 213, 222, 251, 259, 309, 310, 365, 368–370, 601, 643–645, 649–652, 656 603, 620, 621, 623 Cantor set, 643, 645 non-commutative, 619 Cantor’s uniqueness theorem, 498, 640, 641, 650, 652 rational exponents, for, 87, 91 Carleson, Lennart , 655, 656 real exponents, for, 95 Carlson, Fritz, 454, 686 Boas, Ralph, 477 Carson, J. R., 602 Bodenhausen, Rudolf von, 146, 154 Cartier, Pierre, 630, 631 Bohr, Harald, 60, 116, 437, 443, 486–488 Castillione, Johan, 183 Bohr–Mollerup theorem, 486, 488 Cataldi, Pietro Antonio, 61 du Bois-Reymond, Paul, 653 catenary, 145, 146, 153–157, 164, 339 Bolzano, Bernard, 88, 252, 253, 255, 270, 653 Cauchy, Augustin-Louis, 45, 88, 89, 93–96, 98, Bombelli, Rafael, 61 101–103, 120–122, 134, 179, 181, 191, 194, 202, Bombieri, Enrico, 478 203, 211, 251, 252, 254, 255, 263, 267–272, 290, Bonnet, Pierre Ossian, 253–255 337, 366, 374–376, 378, 394, 402, 442, 454, 471, Boole, George, 358, 359, 590, 594, 598, 600–602, 473, 492, 505, 517–520, 523, 543, 544, 560, 561, 624–628, 637, 638 566, 572, 573, 598, 600, 639, 642, 654, 661, 664, Boole summation formula, 594 702 Boros, George, 305 Cauchy product, 94, 97, 101, 102 Bos, Henk, 164 Cavalieri, Bonaventura, 55, 205 Bose,S.N.,360 Cayley, Arthur, 360, 601, 602, 634, 636, 691 Bottazzini, Umberto, 327, 364, 555 Chabert, Jean-Luc, 212 Bouquet, Jean Claude, 337 Chandrasekhar, S., 144, 191 Bourbaki, Nicolas, 60, 164 Chebyshev, Pafnuty, 76, 192, 193, 209–212, 692, Bourget, H., 76 712–720 Boyer, Carl, 21, 35 Chu, Shih-Chieh (also Zhu Shijie), 222 brachistochrone, 157–159, 164 Clairaut, Alexis-Claude, 307, 336, 337, 528, 598 Bradley, Robert E., 103, 638 Clarke, Frances M., 326 Brahmagupta, 20, 21, 80, 188 Clausen, Thomas, 403, 586, 662, 684, 687 Brashman, N. D., 712 Clavis Mathematicae,54 Bressoud, David, 22, 272, 656, 687 Clavius, Christoph, 105 Briggs, Henry, 26, 84, 188–190 Cohen, Henri, 595 Brinkley, John, 612, 613 Collins, John, 58, 85, 167, 168, 189–191, 213, 214, Briot, C., 337 249, 256, 257, 305, 558, 561, 591, 611 Brisson, Barnabe,´ 598 Colson, John, 183 Bromhead, Edward, 599 Commercium Epistolicum, 184, 257, 305 Bronstein, Manuel, 280 condensation test, 101 Bronwin, Brice, 193, 209 Condorcet, Marie-Jean, 40 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-108-70945-3 — Series and Products in the Development of Mathematics Vol 1, 2nd ed. Ranjan Roy Index More Information 752 Index continued fractions definite integral, 363, 679 approximants, 22 hypergeometric, 684, 702–704 convergents, 4, 19, 58, 63, 68 infinite order, 531, 597 divergent series, 225 linear, 331, 343, 353, 684 hypergeometric series, 674, 686 nonhomogeneous, 322, 324, 325, 335, 345, 352 infinite, 57, 61 variable coefficients, 626 infinite products, 466 digamma function, 662 Riccati’s equation, 58, 72 dilogarithm function, 384, 386 series, 68 multivalued, 381 continuous nowhere differentiable function, 253, 653 Dini, Ulisse, 255 Cooke, Roger, 656 Diophantine equations, 4, 301 Cotes, Roger, 58, 72, 190, 192, 207, 275–278, 282, Diophantus, 105 284, 285, 287, 301, 303, 366, 367, 370, 374, 378, Dirac, Paul, 602 380, 440, 598, 611, 620, 689, 691, 693, 694, 697 Dirichlet, Peter Lejeune, 88, 89, 93, 99, 102, 436, 442, Craig, John, 152 443, 470–473, 475, 476, 490, 494, 495, 498, 529, Craik, Alex D., 637 535, 543–545, 547–552, 555, 584, 600, 603, 639, Cramer, Gabriel, 530, 538, 604 663, 665 Crelle, August Leopold, 88, 103, 368, 548, 603 Dirichlet L-function Crelle’s Journal, 88, 103, 139, 368, 544 functional equation, 403 Cuming, Alexander, 500–502 Dirichlet L-series, 88, 286, 406, 433, 435, 442 values of, 406 Damodara, 2 discriminant, 709 Dangerfield, Rodney, 688 Disquisitiones Arithmeticae, 403 Darboux, Gaston, 653, 709, 714 Divergent Series, 601 Dary, Michael, 85 divergent series, 90, 179, 215, 224, 225, 375, 396, Dauben, Joseph W., 656 401, 402, 415, 455, 493, 506, 509, 526, 562, 595, Davis, P. J., 499 601 De Analysi per Aequationes Infinitas, 144, 165, 166, asymptotic, 560 168, 170, 175, 183 Doctrine of Chances, 307, 308, 310, 511 De Computo Serierum, 168, 214, 408 Doetsch, Gustav, 602 De Methodis Serierum et Fluxionum, 144, 147, 167, Dong Youcheng, 668 172, 183, 184 Donkin, William F., 598 De Numeris Triangularibus, 188 Dostrovsky, Sigalia, 363 De Numerosa Potestatum Resolutione, 123 double gamma function, 665 De Quadratura Curvarum, 168, 248, 251, 330, 340 double zeta values, 411, 412, 415 Dedekind, Richard, 65, 102, 103, 255, 256, 270, 378, Duoji Bilei, 668 443, 472, 473, 496, 555, 584, 640, 641, 652 Dedekind cuts, 65 Dutka, J., 499, 687 Descartes, Rene,´ 55, 105–111, 114, 116–118, 123, Dyson, Freeman J., 201, 477, 484 138–140, 143, 151, 161, 313, 328 Dyson’s conjecture, 485 Descartes’s rule of signs, 118, 138 Dyson’s integral, 484 Despeaux, S. E., 638 Dhyanagrahopadesadhyaya, 188 Edwards, A. W. F., 28, 34 Dieudonne,´ Jean, 122, 142 Edwards, Harold, 246 difference equations, 306, 317, 319, 323, 361, 509, Edwards, Joseph, 182, 359, 364 510, 527, 555, 616, 617, 624, 637 Egorov, Dimitri, 654 linear, 306, 307 Einstein, Albert, 360 linear with variable coefficients, 308 Eisenstein, F. Gotthold, 45, 403, 433 nonhomogeneous, 308 elliptic functions, 360 operational method, 597 Ellis, R. Leslie , 600, 602 differential equations, 328–330, 358, 363, 366, 405, Enros, P. C., 638 615, 625, 658, 699, 700 entire functions, 443, 665 adjoint, 336, 350, 351 envelope, 336 algebraic coefficients, 664 Euclid, 117, 124, 143, 193, 668 asymptotic series, 506 Eudoxus, 252 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-108-70945-3 — Series and Products in the Development of Mathematics Vol 1, 2nd ed.
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