Imikorere ya Gamma: Kubona amashusho yimpaka zikomeye

Imikorere ya gamma niyongerekana ryimibare ikomeye yimikorere yibikorwa, isobanurwa kumibare yose igoye usibye imibare itari nziza, kandi iyerekwa ryayo kubintu bigoye byerekana imiterere ya geometrike imurika imiterere yisesengura ryimbitse. Gusobanukirwa uburyo imikorere ya gamma yitwara hejuru yindege igoye ningirakamaro kubibare, abahanga mu bumenyi, naba injeniyeri bishingikiriza kumirima kuva kuri kwantimatike kugeza kuri statistique yerekana imibare.

Ni ubuhe buryo bukomeye imikorere ya Gamma kandi ni ukubera iki bifite akamaro?

Imikorere ya gamma, isobanurwa Γ (z), yatangijwe na Leonhard Euler mu kinyejana cya 18 nkuburyo rusange busanzwe bwibikorwa bifatika kubintu bituzuye. Kubintu byose byiza byuzuye n, Γ (n) = (n - 1)!, Bituma iba ikiraro cyingirakamaro hagati yimibare yihariye nisesengura rihoraho. Indangarugero yacyo igera ku ndege igoye - umwanya-wibice bibiri aho imibare itwara ibice nyabyo nibitekerezo - nibyo rwose nibyo bituma amashusho yayo ashimisha kandi asaba tekiniki.

Kubintu byiza byukuri, imikorere ya gamma itanga umurongo utuje hamwe nuburyo buzwi. Ariko iyo wongereye impaka mu ndege igoye, imyitwarire iba ikize cyane. Inkingi zigaragara kuri zeru na buri kintu cyose cyuzuye, kandi imikorere irerekana imyitwarire ihindagurika nta mugambi-ibiri ushobora gufata neza. Niyo mpamvu abahanga mu mibare bahindukirira amabara ya domaine hamwe nuburinganire bwibice bitatu kugirango bumve neza imikorere ya gamma igoye imiterere yuzuye.

Nigute Imikorere ya Gamma igaragara muburyo bwo gutongana?

Kwiyumvisha imikorere igoye-ifite agaciro k'ibintu bigoye guhinduka mubisanzwe biragoye kuko urimo ukora ibipimo bine bifatika icyarimwe. Tekinike yemewe cyane ni indangarugero ya domaine , aho buri ngingo mumurongo winjiza indege ihabwa ibara ryerekana ibisohoka agaciro. Hue ikubiyemo impaka (inguni) y'ibisohoka, mugihe umucyo cyangwa kwiyuzuzamo bigizwe na modulus (ubunini).

Ibibanza bitatu-byubuso bitanga ubundi buryo bukomeye. Mugutegura modulus | Γ (z) | hejuru yindege igoye, urabona imitwe itangaje kuri pole - iherereye kuri z = 0, −1, −2, −3,… - izamuka igana ubuziraherezo. Hagati yizi nkingi, ibibaya n’imisozi bikurikirana imikorere ya zeru hamwe nintebe zintebe, bigakora imiterere yimibare ari nziza kandi isesengura amakuru.

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Ibikoresho bigezweho byo kubara - Isomero rya Matplotlib ya Python na mpmath, Mathematica, na MATLAB - ryemerera abashakashatsi gutanga aya mashusho neza kandi neza, bigafasha gushakisha uburyo imikorere yitwara nkimpaka zikwirakwira mu ndege igoye.

Nibihe Byibanze Byibanze Byerekanwe Binyuze Kumashusho?

Kwiyumvisha imikorere ya gamma kumpaka zingutu zimurika ibintu byinshi byingenzi bigoye kubyumva neza binyuze muburinganire:

• • Gukomeza gusesengura: Amashusho yerekana nta gushidikanya uburyo imikorere, yabanje gusobanurwa gusa kuri Re (z)> 0, igera mu ndege yose igoye usibye inkingi - ni gihamya yimbaraga zo gukomeza gusesengura.

  Ni ubuhe butumwa bukubiye mu mateka n'ihindagurika ry'ubushakashatsi bw'imikorere ya Gamma?

  Ibisobanuro byumwimerere bya Euler, Γ (z) = ∫₀ ^ ∞ t ^ (z - 1) e ^ (- t) dt, yashinze umusingi mu 1729. Gauss, Legendre, na Weierstrass buri wese yagize uruhare mu ivugurura - ifishi y’ibicuruzwa bya Weierstrass ifite ubushishozi bwo gusobanukirwa imiterere yinkingi. Mu kinyejana cya 20, isesengura rinini ryashyizeho uburyo bwo gusobanukirwa imikorere ya gamma nkigikorwa cya meromorphic, kandi sisitemu ya algebra ya mudasobwa igezweho yahinduye iyerekwa riva mu bigereranyo byashushanijwe mu buryo bukomeye, bushushanya.

  Ubwihindurize bwo kubara amashusho yatumye imikorere ya gamma igera kurenza imibare yuzuye. Uyu munsi, igaragara muburyo busanzwe bwo gukwirakwiza amahirwe (gukwirakwiza gamma na beta), mubisubizo byuburinganire butandukanye muri fiziki, no mubitekerezo byumubare binyuze mubikorwa byayo na Riemann zeta - buri domeni yungukirwa nubushishozi butanga amashusho.

  Nigute Imikorere ya Gamma Igikorwa Igaragara ikoreshwa mubikorwa bigezweho?

  Ibikorwa bifatika byimikorere ya gamma iyerekwa irenze imibare yimibare. Muri comptabilite y'ibarurishamibare, kwiyumvisha imikorere ya gamma bifasha abahanga mu bumenyi gusobanukirwa umwanya wimiterere ya moderi yagabanijwe ikoreshwa muri siyanse ya actuarial, théorie de ligue, hamwe nisesengura rya Bayesian. Mubitekerezo bya kwantum, kubara Feynman kubara kenshi bikubiyemo gusuzuma imikorere ya gamma kumpaka zitoroshye, kandi visualisation ifasha abahanga mubya fiziki kugenzura imyitwarire idahwitse. Mugutunganya ibimenyetso, imikorere igaragara mugushushanya no kubara ibice, aho imyitwarire yayo igoye-indege igira ingaruka zisesengura sisitemu ihamye.

  Amashyirahamwe akorana numuyoboro utoroshye wamakuru hamwe nisesengura ryakazi bigenda bikenera urubuga rushobora guhuza ibyo bikoresho bihanitse nibisohoka. Aha niho rwose sisitemu yubucuruzi yuzuye iba ingirakamaro - ntabwo ari mumatsinda yubushakashatsi gusa, ahubwo no mumuryango uwo ariwo wose ucunga imishinga itandukanye kurwego.

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  Ibibazo bikunze kubazwa

  Kuki imikorere ya gamma ifite inkingi kumubare utari mwiza?

  . Iyi nkingi yoroshye ifite ibisigisigi byatanzwe na (−1) ^ n / n!, Ukuri kugaragara neza mumashusho yerekana amabara.

  Nibihe bikoresho bya software nibyiza mugushushanya imikorere ya gamma hejuru yimpaka zoroshye?

  Isomero rya mpmath isomero rihujwe na Matplotlib niryo hitamo ryoroshye kubashakashatsi, ritanga isuzumabumenyi-ridasubirwaho hamwe na gahunda yo gutegura byoroshye. Mathematica itanga ibikorwa byubatswe byimikorere itegura hamwe na domaine ibara hanze. Kubikorwa, gushakisha-gushakisha gushakisha, ibikoresho nka Indorerezi cyangwa Igicu cya Wolfram cyemerera igihe nyacyo cyo guhanagura. Agasanduku k'ibikoresho by'ikigereranyo ka MATLAB gakundwa muburyo bwa injeniyeri aho hakenewe guhuza imiyoboro minini yo kwigana.

  Nigute imikorere ya gamma ihuza imikorere ya Riemann zeta?

  Ihuza ritangwa nuburinganire bwimikorere ya Riemann zeta imikorere: ζ (s) = 2 ^ s π ^ (s - 1) icyaha (πs / 2) Γ (1 - s) ζ (1 - s). Iri gereranya rikoresha imikorere ya gamma kugirango ihuze indangagaciro zeta kumpande zinyuranye zumurongo wingenzi Re (s) = 1/2. Kwiyumvisha imikorere yombi hejuru yindege igoye kuruhande byerekana uburyo imikorere ya gamma inkingi na zeru zeru zeru bihuza cyane, umubano kumutima wa Hypothesis ya Riemann idakemutse.

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  Waba uri umushakashatsi uhuza imishinga igoye yimibare, itsinda ryubumenyi bwamakuru acunga ibikorwa byisesengura, cyangwa ishyirahamwe ryapima ibikorwa mubice byinshi, ufite urubuga rwiza rutanga itandukaniro. Mewayz niyo yose-imwe-imwe yubucuruzi OS yizewe nabakoresha barenga 138.000, itanga module 207 ihuriweho kugirango yorohereze ibintu byose uhereye kubuyobozi bwumushinga kugeza kubufatanye bwamakipe - guhera kumadorari 19 / ukwezi. Witeguye kuzana ibisobanuro n'imiterere kumurimo utoroshye? Tangira urugendo rwawe kuri app.mewayz.com kandi wibonere inzira nziza yo gukora.