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Euler–Poisson–Darboux equation

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Shishkina, Elina L.; Sitnik, Sergei M. (2017-07-15). "The general form of the Euler--Poisson--Darboux equation and application of transmutation method".
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Fusaro, B. A. (1966). "A Solution of a Singular, Mixed Problem for the Equation of Euler-Poisson- Darboux (EPD)".
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Copson, E. T. (1956-06-12). "On a regular Cauchy problem for the Euler—Poisson—Darboux equation".
841: 747: 579: 718: 773: 476:"On a Cauchy problem for a generalized Euler-Poisson-Darboux equation with polyharmonic data" 487: 401: 324:
and some sources quote this equation when referring to the Euler–Poisson–Darboux equation.
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Cambridge: Cambridge University Press. 553: 819: 514: 391: 358: 575: 760: 354: 352: 13: 654:Euler's continued fraction formula 601: 14: 858: 679:Euler's pump and turbine equation 547: 517:The American Mathematical Monthly 480:Journal of Differential Equations 349: 764: 742: 741: 699:Euler equations (fluid dynamics) 689:Euler's sum of powers conjecture 556:"Euler–Poisson–Darboux equation" 317:{\displaystyle N={\frac {m}{2}}} 474:Miles, E.P; Young, E.C (1966). 837:Partial differential equations 832:Eponymous equations of physics 639:Euler–Poisson–Darboux equation 508: 467: 446: 385: 361:Partial differential equations 88: 62: 1: 345:. Academic Press, Boston, MA. 327: 26:partial differential equation 780:. You can help Knowledge by 669:Euler's four-square identity 501:10.1016/0022-0396(66)90056-8 143:This equation is related to 7: 847:Mathematical analysis stubs 724:Euler–Bernoulli beam theory 561:Encyclopedia of Mathematics 124:This equation is named for 10: 863: 759: 737: 634:Euler–Mascheroni constant 609: 684:Euler's rotation theorem 644:Euler–Rodrigues formula 624:Euler–Maclaurin formula 614:Euler–Lagrange equation 423:2027/mdp.39015095254382 341:Zwillinger, D. (1997). 776:–related article is a 719:Euler number (physics) 649:Euler–Tricomi equation 554:Moroşanu, C. (2001) , 414:10.1098/rspa.1956.0106 359:Copson, E. T. (1975). 318: 285: 253: 218: 115: 827:Differential calculus 774:mathematical analysis 659:Euler's critical load 629:Euler–Maruyama method 394:Proc. R. Soc. Lond. A 319: 286: 284:{\displaystyle y=r-t} 254: 252:{\displaystyle x=r+t} 219: 116: 22:Euler–Poisson–Darboux 619:Euler–Lotka equation 295: 263: 231: 150: 34: 492:1966JDE.....2..482M 406:1956RSPSA.235..560C 314: 281: 249: 214: 111: 789: 788: 757: 756: 400:(1203): 560–572. 312: 177: 103: 854: 810: 803: 796: 768: 761: 745: 744: 674:Euler's identity 596: 589: 582: 573: 572: 568: 541: 540: 512: 506: 505: 503: 471: 465: 464: 462: 450: 444: 443: 425: 389: 383: 382: 356: 347: 346: 338: 323: 321: 320: 315: 313: 305: 290: 288: 287: 282: 258: 256: 255: 250: 223: 221: 220: 215: 204: 203: 188: 187: 178: 170: 165: 164: 120: 118: 117: 112: 104: 102: 91: 87: 86: 74: 73: 57: 52: 51: 24:equation is the 862: 861: 857: 856: 855: 853: 852: 851: 817: 816: 815: 814: 758: 753: 733: 694:Euler's theorem 664:Euler's formula 605: 600: 550: 545: 544: 529:10.2307/2314793 513: 509: 472: 468: 451: 447: 390: 386: 371: 357: 350: 339: 335: 330: 304: 296: 293: 292: 264: 261: 260: 232: 229: 228: 196: 192: 183: 179: 169: 157: 153: 151: 148: 147: 92: 82: 78: 69: 65: 58: 56: 41: 37: 35: 32: 31: 12: 11: 5: 860: 850: 849: 844: 842:Leonhard Euler 839: 834: 829: 813: 812: 805: 798: 790: 787: 786: 769: 755: 754: 752: 751: 738: 735: 734: 732: 731: 726: 721: 716: 711: 706: 704:Euler function 701: 696: 691: 686: 681: 676: 671: 666: 661: 656: 651: 646: 641: 636: 631: 626: 621: 616: 610: 607: 606: 603:Leonhard Euler 599: 598: 591: 584: 576: 570: 569: 549: 548:External links 546: 543: 542: 523:(6): 610–613. 507: 486:(4): 482–487. 466: 445: 384: 370:978-0521098939 369: 348: 332: 331: 329: 326: 311: 308: 303: 300: 280: 277: 274: 271: 268: 248: 245: 242: 239: 236: 225: 224: 213: 210: 207: 202: 199: 195: 191: 186: 182: 176: 173: 168: 163: 160: 156: 134:Gaston Darboux 130:Leonhard Euler 126:Siméon Poisson 122: 121: 110: 107: 101: 98: 95: 90: 85: 81: 77: 72: 68: 64: 61: 55: 50: 47: 44: 40: 9: 6: 4: 3: 2: 859: 848: 845: 843: 840: 838: 835: 833: 830: 828: 825: 824: 822: 811: 806: 804: 799: 797: 792: 791: 785: 783: 779: 775: 770: 767: 763: 762: 750: 749: 740: 739: 736: 730: 727: 725: 722: 720: 717: 715: 714:Euler numbers 712: 710: 707: 705: 702: 700: 697: 695: 692: 690: 687: 685: 682: 680: 677: 675: 672: 670: 667: 665: 662: 660: 657: 655: 652: 650: 647: 645: 642: 640: 637: 635: 632: 630: 627: 625: 622: 620: 617: 615: 612: 611: 608: 604: 597: 592: 590: 585: 583: 578: 577: 574: 567: 563: 562: 557: 552: 551: 538: 534: 530: 526: 522: 518: 511: 502: 497: 493: 489: 485: 481: 477: 470: 461: 456: 449: 441: 437: 433: 429: 424: 419: 415: 411: 407: 403: 399: 395: 388: 380: 376: 372: 366: 362: 355: 353: 344: 337: 333: 325: 309: 306: 301: 298: 278: 275: 272: 269: 266: 246: 243: 240: 237: 234: 211: 208: 205: 200: 197: 193: 189: 184: 180: 174: 171: 166: 161: 158: 154: 146: 145: 144: 141: 139: 138:wave equation 135: 131: 127: 108: 105: 99: 96: 93: 83: 79: 75: 70: 66: 59: 53: 48: 45: 42: 38: 30: 29: 28: 27: 23: 19: 782:expanding it 771: 746: 709:Euler method 638: 559: 520: 516: 510: 483: 479: 469: 448: 397: 393: 387: 360: 342: 336: 226: 142: 123: 21: 15: 18:mathematics 821:Categories 460:1707.04733 328:References 729:Namesakes 566:EMS Press 440:122720337 432:0080-4630 276:− 190:− 748:Category 291:, where 537:2314793 488:Bibcode 402:Bibcode 379:1499723 535:  438:  430:  377:  367:  132:, and 20:, the 772:This 533:JSTOR 455:arXiv 436:S2CID 778:stub 428:ISSN 375:OCLC 365:ISBN 525:doi 496:doi 418:hdl 410:doi 398:235 227:by 16:In 823:: 564:, 558:, 531:. 521:73 519:. 494:. 482:. 478:. 434:. 426:. 416:. 408:. 396:. 373:. 351:^ 259:, 140:. 128:, 109:0. 809:e 802:t 795:v 784:. 595:e 588:t 581:v 539:. 527:: 504:. 498:: 490:: 484:2 463:. 457:: 442:. 420:: 412:: 404:: 381:. 310:2 307:m 302:= 299:N 279:t 273:r 270:= 267:y 247:t 244:+ 241:r 238:= 235:x 212:, 209:0 206:= 201:t 198:t 194:u 185:r 181:u 175:r 172:m 167:+ 162:r 159:r 155:u 106:= 100:y 97:+ 94:x 89:) 84:y 80:u 76:+ 71:x 67:u 63:( 60:N 54:+ 49:y 46:, 43:x 39:u

Index

mathematics
partial differential equation
Siméon Poisson
Leonhard Euler
Gaston Darboux
wave equation


ISBN
978-0521098939
OCLC
1499723
Bibcode
1956RSPSA.235..560C
doi
10.1098/rspa.1956.0106
hdl
2027/mdp.39015095254382
ISSN
0080-4630
S2CID
122720337
arXiv
1707.04733
"On a Cauchy problem for a generalized Euler-Poisson-Darboux equation with polyharmonic data"
Bibcode
1966JDE.....2..482M
doi
10.1016/0022-0396(66)90056-8
doi

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