Knowledge

File:ChebyshevPsi.png

Source 📝

614:"}},"text\/plain":{"en":{"":"checksum"}}},"{\"value\":\"26a75e3a111a086905d9fb591f6cb648a29f9b52\",\"type\":\"string\"}":{"text\/html":{"en":{"P4092":"26a75e3a111a086905d9fb591f6cb648a29f9b52"}},"text\/plain":{"en":{"P4092":"26a75e3a111a086905d9fb591f6cb648a29f9b52"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":459,\"id\":\"P459\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":" 538:"}},"text\/plain":{"en":{"":"inception"}}},"{\"value\":{\"time\":\"+2006-07-02T00:00:00Z\",\"timezone\":0,\"before\":0,\"after\":0,\"precision\":11,\"calendarmodel\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q1985727\"},\"type\":\"time\"}":{"text\/html":{"en":{"P571":"2 July 2006"}},"text\/plain":{"en":{"P571":"2 July 2006"}}}}": --> 610: 333: 67: 618:"}},"text\/plain":{"en":{"":"determination method"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":13414952,\"id\":\"Q13414952\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P459":" 450:"}},"text\/plain":{"en":{"":"copyright license"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":98592850,\"id\":\"Q98592850\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P275":" 406:"}},"text\/plain":{"en":{"":"copyright status"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":88088423,\"id\":\"Q88088423\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P6216":" 576:"}},"text\/plain":{"en":{"":"media type"}}},"{\"value\":\"image\\\/png\",\"type\":\"string\"}":{"text\/html":{"en":{"P1163":"image\/png"}},"text\/plain":{"en":{"P1163":"image\/png"}}}}": --> 494:"}},"text\/plain":{"en":{"":"source of file"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":66458942,\"id\":\"Q66458942\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P7482":" 681:"}},"text\/plain":{"en":{"":"data size"}}},"{\"value\":{\"amount\":\"+6860\",\"unit\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q8799\"},\"type\":\"quantity\"}":{"text\/html":{"en":{"P3575":"6,860 726:"}},"text\/plain":{"en":{"":"height"}}},"{\"value\":{\"amount\":\"+308\",\"unit\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q355198\"},\"type\":\"quantity\"}":{"text\/html":{"en":{"P2048":"308 771:"}},"text\/plain":{"en":{"":"width"}}},"{\"value\":{\"amount\":\"+499\",\"unit\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q355198\"},\"type\":\"quantity\"}":{"text\/html":{"en":{"P2049":"499 767: 38: 619: 495: 451: 407: 240: 768: 723: 678: 611: 573: 491: 403: 615: 535: 447: 871:
Plot of Chebyshev's <math>\psi</math> function, along with the approximation <math>x-\log 2\pi</math>. This function can be defined in
205: 136:
for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
410:"}},"text\/plain":{"en":{"P6216":"copyrighted, dedicated to the public domain by copyright holder"}}}}": --> 454:"}},"text\/plain":{"en":{"P275":"released into the public domain by the copyright holder"}}}}": --> 133: 663: 521: 477: 433: 254:
Plot, n - Log}, {n, 0, 50}, AxesLabel -> {n, "ψ(n)"}, TextStyle -> {FontFamily -> "Times", FontSize -> 16},
782: 737: 692: 629: 583: 505: 417: 498:"}},"text\/plain":{"en":{"P7482":"original creation by uploader"}}}}": --> 153: 139: 907: 656: 545: 461: 392: 78: 46: 293: 127: 927: 685:"}},"text\/plain":{"en":{"P3575":"6,860 byte"}}}}": --> 957: 775:"}},"text\/plain":{"en":{"P2049":"499 pixel"}}}}": --> 730:"}},"text\/plain":{"en":{"P2048":"308 pixel"}}}}": --> 210: 86: 622:"}},"text\/plain":{"en":{"P459":"SHA-1"}}}}": --> 190: 8: 289: 889: 340: 73: 382: 123: 853: 848: 37: 285: 864: 157: 152:
It is recommended to name the SVG file “ChebyshevPsi.svg”—then the template
792: 747: 702: 639: 593: 555: 515: 471: 427: 243: 872: 875:
by: ψ := Sum, Floor/Log] Log, 0], {p, 2, n}] SetAttributes[ψ, Listabl
355:, without any conditions, unless such conditions are required by law. 917: 937: 821:
Click on a date/time to view the file as it appeared at that time.
338:
I, the copyright holder of this work, release this work into the
947: 434:
copyrighted, dedicated to the public domain by copyright holder
408:
copyrighted, dedicated to the public domain by copyright holder
248:ψ := Sum, Floor/Log] Log, 0], {p, 2, n}] SetAttributes 347:
In some countries this may not be legally possible; if so:
265: 61: 478:
released into the public domain by the copyright holder
452:
released into the public domain by the copyright holder
376:
Add a one-line explanation of what this file represents
883: 213: 193: 898: 819: 85:
Commons is a freely licensed media file repository.
234: 199: 256:PlotStyle -> {{Hue, Thickness}, {RGBColor}}] 51:(499 × 308 pixels, file size: 7 KB, MIME type: 66: 261: 174: 281: 271: 14: 772: 727: 682: 351:I grant anyone the right to use this work 900:The following other wikis use this file: 645:26a75e3a111a086905d9fb591f6cb648a29f9b52 132:. This has several advantages; see  207:function, along with the approximation 251:The above plot was then generated by: 332: 97: 327: 104: 885:The following page uses this file: 812: 13: 381: 375: 242:. This function can be defined in 181: 115: 98: 44: 971: 380: 366: 331: 108: 65: 31: 21: 363: 182: 41:No higher resolution available. 895: 816: 362: 26: 1: 522:original creation by uploader 496:original creation by uploader 880: 388:Items portrayed in this file 303: 235:{\displaystyle x-\log 2\pi } 7: 10: 976: 954:Usage on zh.wikipedia.org 944:Usage on pl.wikipedia.org 934:Usage on fr.wikipedia.org 924:Usage on fa.wikipedia.org 914:Usage on ca.wikipedia.org 904:Usage on ar.wikipedia.org 171: 120:image could be re-created 100: 813: 344:. This applies worldwide. 275: 134:Commons:Media for cleanup 16: 365: 154:Vector version available 140:vector version available 72:This is a file from the 36: 870: 264: 76:. Information from its 938:Fonction de Tchebychev 236: 201: 79:description page there 237: 202: 200:{\displaystyle \psi } 657:determination method 616:determination method 211: 191: 187:Plot of Chebyshev's 160:) does not need the 948:Funkcja Czebyszewa 918:Funció de Txebixov 890:Chebyshev function 849:17:25, 2 July 2006 232: 197: 896:Global file usage 878: 774: 729: 684: 462:copyright license 448:copyright license 374: 360: 359: 348: 326: 325: 300: 299: 169: 168: 94: 93: 74:Wikimedia Commons 32:Global file usage 967: 861: 823: 801: 756: 711: 666: 661: 418:copyright status 404:copyright status 372: 346: 335: 334: 328: 322: 319: 316: 313: 308: 307: 277: 267: 241: 239: 238: 233: 206: 204: 203: 198: 186: 178: 177:ChebyshevPsi.png 172: 147: 112: 111: 105: 90: 69: 68: 62: 56: 54: 47:ChebyshevPsi.png 975: 974: 970: 969: 968: 966: 965: 964: 894: 879: 867: 859: 815: 814: 811: 810: 809: 808: 807: 806: 805: 804: 802: 799: 789: 788: 787: 785: 766: 765: 764: 763: 762: 761: 760: 759: 757: 754: 744: 743: 742: 740: 721: 720: 719: 718: 717: 716: 715: 714: 712: 709: 699: 698: 697: 695: 676: 675: 674: 673: 672: 671: 670: 669: 668: 667: 662: 659: 650: 649: 648: 646: 636: 635: 634: 632: 609: 608: 607: 606: 605: 604: 603: 602: 600: 590: 589: 588: 586: 571: 570: 569: 568: 567: 566: 565: 564: 562: 552: 551: 550: 548: 533: 532: 531: 530: 529: 528: 527: 526: 524: 512: 511: 510: 508: 489: 488: 487: 486: 485: 484: 483: 482: 480: 468: 467: 466: 464: 445: 444: 443: 442: 441: 440: 439: 438: 436: 424: 423: 422: 420: 401: 400: 399: 398: 397: 395: 379: 378: 377: 353:for any purpose 320: 317: 314: 311: 306: 301: 257: 255: 249: 212: 209: 208: 192: 189: 188: 176: 165: 137: 124:vector graphics 109: 103: 96: 95: 84: 83: 82:is shown below. 58: 52: 50: 43: 42: 12: 11: 5: 973: 963: 962: 961: 960: 952: 951: 950: 942: 941: 940: 932: 931: 930: 922: 921: 920: 912: 911: 910: 897: 893: 892: 882: 877: 876: 869: 865: 862: 856: 851: 846: 842: 841: 838: 835: 832: 829: 826: 818: 803: 797: 795: 794: 793: 791: 790: 786: 781: 779: 778: 777: 776: 770: 758: 752: 750: 749: 748: 746: 745: 741: 736: 734: 733: 732: 731: 725: 713: 707: 705: 704: 703: 701: 700: 696: 691: 689: 688: 687: 686: 680: 655: 654: 653: 652: 651: 647: 644: 642: 641: 640: 638: 637: 633: 628: 626: 625: 624: 623: 621: 617: 613: 601: 598: 596: 595: 594: 592: 591: 587: 582: 580: 579: 578: 577: 575: 563: 560: 558: 557: 556: 554: 553: 549: 544: 542: 541: 540: 539: 537: 525: 520: 518: 517: 516: 514: 513: 509: 506:source of file 504: 502: 501: 500: 499: 497: 493: 492:source of file 481: 476: 474: 473: 472: 470: 469: 465: 460: 458: 457: 456: 455: 453: 449: 437: 432: 430: 429: 428: 426: 425: 421: 416: 414: 413: 412: 411: 409: 405: 396: 391: 389: 386: 385: 384: 383: 371: 370: 367: 364: 358: 357: 336: 324: 323: 305: 302: 298: 297: 283: 279: 278: 273: 269: 268: 263: 259: 258: 253: 247: 231: 228: 225: 222: 219: 216: 196: 179: 170: 167: 166: 162:new image name 144:new image name 113: 102: 99: 92: 91: 70: 60: 59: 40: 35: 34: 29: 24: 19: 9: 6: 4: 3: 2: 972: 959: 956: 955: 953: 949: 946: 945: 943: 939: 936: 935: 933: 929: 926: 925: 923: 919: 916: 915: 913: 909: 908:دالة تشيبيشيف 906: 905: 903: 902: 901: 891: 888: 887: 886: 874: 868: 863: 857: 855: 852: 850: 847: 844: 843: 839: 836: 833: 830: 827: 825: 824: 822: 796: 784: 780: 751: 739: 735: 706: 694: 690: 665: 658: 643: 631: 627: 597: 585: 581: 559: 547: 543: 523: 519: 507: 503: 479: 475: 463: 459: 435: 431: 419: 415: 394: 390: 387: 368: 361: 356: 354: 349: 345: 343: 342: 341:public domain 337: 330: 329: 315:Public domain 312:Public domain 310: 309: 295: 291: 287: 284: 280: 274: 270: 260: 252: 245: 244:w:Mathematica 229: 226: 223: 220: 217: 214: 194: 185: 180: 173: 163: 159: 155: 151: 150: 145: 141: 135: 131: 129: 125: 119: 114: 107: 106: 88: 81: 80: 75: 71: 64: 63: 57: 48: 39: 33: 30: 28: 25: 23: 20: 18: 15: 899: 884: 820: 817:File history 352: 350: 339: 250: 183: 161: 149: 143: 121: 117: 87:You can help 77: 45: 22:File history 873:Mathematica 561:2 July 2006 266:2 July 2006 175:Description 928:تابع چبیشف 881:File usage 858:499 × 308 834:Dimensions 584:media type 574:media type 164:parameter. 27:File usage 831:Thumbnail 828:Date/Time 693:data size 679:data size 599:image/png 546:inception 536:inception 304:Licensing 184:English: 53:image/png 866:Dantheox 630:checksum 612:checksum 369:Captions 286:Dantheox 276:Own work 845:current 840:Comment 393:depicts 373:English 294:Uploads 101:Summary 49:‎ 958:切比雪夫函數 860:(7 KB) 738:height 724:height 708:6,860 282:Author 272:Source 126:as an 122:using 800:pixel 783:width 773:pixel 769:width 755:pixel 728:pixel 664:SHA-1 620:SHA-1 321:false 318:false 118:graph 116:This 837:User 798:499 753:308 710:byte 683:byte 290:talk 262:Date 246:by: 156:(or 130:file 17:File 292:) ( 221:log 158:Vva 128:SVG 660:: 230:π 224:⁡ 218:− 195:ψ 146:}} 138:{{ 296:) 288:( 227:2 215:x 148:. 142:| 89:. 55:)

Index

File
File history
File usage
Global file usage
File:ChebyshevPsi.png
ChebyshevPsi.png
Wikimedia Commons
description page there
You can help
vector graphics
SVG
Commons:Media for cleanup
vector version available
Vector version available
Vva
w:Mathematica
Dantheox
talk
Uploads
public domain
depicts
copyright status<\/a>"}},"text\/plain":{"en":{"":"copyright status"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":88088423,\"id\":\"Q88088423\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P6216":"copyrighted, dedicated to the public domain by copyright holder<\/a>"}},"text\/plain":{"en":{"P6216":"copyrighted, dedicated to the public domain by copyright holder"}}}}">

copyright status
copyrighted, dedicated to the public domain by copyright holder
copyright license<\/a>"}},"text\/plain":{"en":{"":"copyright license"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":98592850,\"id\":\"Q98592850\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P275":"released into the public domain by the copyright holder<\/a>"}},"text\/plain":{"en":{"P275":"released into the public domain by the copyright holder"}}}}">

copyright license
released into the public domain by the copyright holder
source of file<\/a>"}},"text\/plain":{"en":{"":"source of file"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":66458942,\"id\":\"Q66458942\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P7482":"original creation by uploader<\/a>"}},"text\/plain":{"en":{"P7482":"original creation by uploader"}}}}">

source of file
original creation by uploader
inception<\/a>"}},"text\/plain":{"en":{"":"inception"}}},"{\"value\":{\"time\":\"+2006-07-02T00:00:00Z\",\"timezone\":0,\"before\":0,\"after\":0,\"precision\":11,\"calendarmodel\":\"http:\\\/\\\/www.wikidata.org\\\/entity\\\/Q1985727\"},\"type\":\"time\"}":{"text\/html":{"en":{"P571":"2 July 2006"}},"text\/plain":{"en":{"P571":"2 July 2006"}}}}">

inception
media type<\/a>"}},"text\/plain":{"en":{"":"media type"}}},"{\"value\":\"image\\\/png\",\"type\":\"string\"}":{"text\/html":{"en":{"P1163":"image\/png"}},"text\/plain":{"en":{"P1163":"image\/png"}}}}">

media type
checksum<\/a>"}},"text\/plain":{"en":{"":"checksum"}}},"{\"value\":\"26a75e3a111a086905d9fb591f6cb648a29f9b52\",\"type\":\"string\"}":{"text\/html":{"en":{"P4092":"26a75e3a111a086905d9fb591f6cb648a29f9b52"}},"text\/plain":{"en":{"P4092":"26a75e3a111a086905d9fb591f6cb648a29f9b52"}}},"{\"value\":{\"entity-type\":\"property\",\"numeric-id\":459,\"id\":\"P459\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"":"determination method<\/a>"}},"text\/plain":{"en":{"":"determination method"}}},"{\"value\":{\"entity-type\":\"item\",\"numeric-id\":13414952,\"id\":\"Q13414952\"},\"type\":\"wikibase-entityid\"}":{"text\/html":{"en":{"P459":"SHA-1<\/a>"}},"text\/plain":{"en":{"P459":"SHA-1"}}}}">

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.