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Continuous q-Legendre polynomials

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503: 22: 76: 413: 172: 408:{\displaystyle P_{n}(x|q)={}_{4}\phi _{3}\left(q^{-n},q^{n+1},q^{\frac {1}{4}}e^{i\theta },q^{\frac {1}{4}}e^{-i\theta };q,-q^{-{\frac {1}{2}}},-q;q,q\right),\quad x=\cos \,\theta .} 97: 573: 544: 453: 121: 563: 537: 163: 578: 530: 480: 143: 51: 485: 568: 449: 441: 32: 463: 459: 514: 90: 84: 557: 147: 502: 510: 445: 41: 440:, Springer Monographs in Mathematics, Berlin: Springer-Verlag, p. 14, 21: 69: 15: 432:
Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F. (2010),
518: 102: 46: 36: 175: 151: 407: 434:Hypergeometric orthogonal polynomials and their 538: 8: 477:Moments of Classical Orthogonal Polynomials 545: 531: 154:give a detailed list of their properties. 484: 398: 347: 343: 315: 300: 284: 269: 250: 234: 219: 209: 207: 192: 180: 174: 122:Learn how and when to remove this message 424: 162:The polynomials are given in terms of 152:Koekoek, Lesky & Swarttouw (2010) 142:are a family of basic hypergeometric 7: 499: 497: 14: 574:Special hypergeometric functions 501: 74: 20: 388: 200: 193: 186: 164:basic hypergeometric functions 1: 479:(Ph.D.). Universität Kassel. 517:. You can help Knowledge by 595: 496: 475:Sadjang, Patrick Njionou. 446:10.1007/978-3-642-05014-5 35:, as no other articles 564:Orthogonal polynomials 513:-related article is a 409: 144:orthogonal polynomials 83:This article includes 410: 140:-Legendre polynomials 173: 134:In mathematics, the 405: 91:properly formatted 54:for suggestions. 44:to this page from 526: 525: 455:978-3-642-05013-8 355: 308: 277: 132: 131: 124: 68: 67: 586: 579:Polynomial stubs 547: 540: 533: 505: 498: 490: 488: 467: 466: 429: 414: 412: 411: 406: 384: 380: 358: 357: 356: 348: 326: 325: 310: 309: 301: 292: 291: 279: 278: 270: 261: 260: 242: 241: 224: 223: 214: 213: 208: 196: 185: 184: 127: 120: 116: 113: 107: 105: 100:this article by 85:inline citations 78: 77: 70: 63: 60: 49: 47:related articles 24: 16: 594: 593: 589: 588: 587: 585: 584: 583: 554: 553: 552: 551: 494: 486:10.1.1.643.3896 474: 471: 470: 456: 431: 430: 426: 421: 339: 311: 296: 280: 265: 246: 230: 229: 225: 215: 206: 176: 171: 170: 160: 128: 117: 111: 108: 103:correcting them 101: 95: 79: 75: 64: 58: 55: 45: 42:introduce links 25: 12: 11: 5: 592: 590: 582: 581: 576: 571: 566: 556: 555: 550: 549: 542: 535: 527: 524: 523: 506: 492: 491: 469: 468: 454: 423: 422: 420: 417: 416: 415: 404: 401: 397: 394: 391: 387: 383: 379: 376: 373: 370: 367: 364: 361: 354: 351: 346: 342: 338: 335: 332: 329: 324: 321: 318: 314: 307: 304: 299: 295: 290: 287: 283: 276: 273: 268: 264: 259: 256: 253: 249: 245: 240: 237: 233: 228: 222: 218: 212: 205: 202: 199: 195: 191: 188: 183: 179: 159: 156: 130: 129: 82: 80: 73: 66: 65: 59:September 2018 52:Find link tool 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 591: 580: 577: 575: 572: 570: 567: 565: 562: 561: 559: 548: 543: 541: 536: 534: 529: 528: 522: 520: 516: 512: 507: 504: 500: 495: 487: 482: 478: 473: 472: 465: 461: 457: 451: 447: 443: 439: 435: 428: 425: 418: 402: 399: 395: 392: 389: 385: 381: 377: 374: 371: 368: 365: 362: 359: 352: 349: 344: 340: 336: 333: 330: 327: 322: 319: 316: 312: 305: 302: 297: 293: 288: 285: 281: 274: 271: 266: 262: 257: 254: 251: 247: 243: 238: 235: 231: 226: 220: 216: 210: 203: 197: 189: 181: 177: 169: 168: 167: 165: 157: 155: 153: 149: 146:in the basic 145: 141: 139: 126: 123: 115: 104: 99: 94: 92: 89:they are not 86: 81: 72: 71: 62: 53: 48: 43: 39: 38: 34: 29:This article 27: 23: 18: 17: 519:expanding it 508: 493: 476: 437: 433: 427: 161: 148:Askey scheme 137: 135: 133: 118: 109: 88: 56: 30: 136:continuous 558:Categories 511:polynomial 438:-analogues 419:References 158:Definition 50:; try the 37:link to it 569:Q-analogs 481:CiteSeerX 400:θ 363:− 345:− 337:− 323:θ 317:− 289:θ 236:− 217:ϕ 40:. Please 112:May 2024 464:2656096 98:improve 96:Please 483:  462:  452:  87:, but 33:orphan 31:is an 509:This 515:stub 450:ISBN 442:doi 396:cos 166:by 560:: 460:MR 458:, 448:, 546:e 539:t 532:v 521:. 489:. 444:: 436:q 403:. 393:= 390:x 386:, 382:) 378:q 375:, 372:q 369:; 366:q 360:, 353:2 350:1 341:q 334:, 331:q 328:; 320:i 313:e 306:4 303:1 298:q 294:, 286:i 282:e 275:4 272:1 267:q 263:, 258:1 255:+ 252:n 248:q 244:, 239:n 232:q 227:( 221:3 211:4 204:= 201:) 198:q 194:| 190:x 187:( 182:n 178:P 150:. 138:q 125:) 119:( 114:) 110:( 106:. 93:. 61:) 57:(

Index


orphan
link to it
introduce links
related articles
Find link tool
inline citations
properly formatted
improve
correcting them
Learn how and when to remove this message
orthogonal polynomials
Askey scheme
Koekoek, Lesky & Swarttouw (2010)
basic hypergeometric functions
doi
10.1007/978-3-642-05014-5
ISBN
978-3-642-05013-8
MR
2656096
CiteSeerX
10.1.1.643.3896
Stub icon
polynomial
stub
expanding it
v
t
e

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