Wp/shi/Tanfalit n Stirling

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Amgrad ad icqqa ad t tfhmt !
amgrad-ad gis kra n iwalwn nna ur iẓḍaṛ ad tn ifhm yan iɣ ur issinn ɣ umawal iẓlin n tutlayt taclḥiyt tatrart.
Mad igan afssay ? Fad ad tfhmt mad gis illan tzḍart ad tawst i yixf nnk s umawal lli illan ɣ izddar akkʷ n tasna. Iɣ t ur tufit, tzḍart ad nn taggʷt ɣ imawaln d isgzawaln.
Mplwp factorial gamma stirling.svg

Tanfalit n StirlingTamawaẓt n Stirling tga ɣ tusnakt, yat tnfalit nna yakkan agdazal n uskir n yan umḍan ummid agaman iɣ yaẓ i wartmi:

nna nttafa tettyura ula s tɣarast ad:

maɣ ɣid tga amḍan n tusnakt ikspununsyal.

Amzruy

Brahim du Mwavr ad akk izwarn is yufa tanfalit ad ddaw-as:

maɣ tga yat timzgit tilawt (ur igaddan d amya)

Mad ifka nɣ mad izayd Stirling i tanfalit ad iga-tt atig n timzgit, iga y'as fad ad aɣ tfk asbuɣlu n i kraygat amizzwr.

Atig ɣ wartmi

Bac ad nit ntḥqqaq is nit ar ttaẓ tanfalit ad i atig n , nẓḍar ad nɛdl taflwit ad lli aɣ immaln atign n d win s sin-itsn:

n n !
1 1 0,92 0,999
2 2 1,92 1,999
3 6 5,84 5,998
4 24 23,51 23,996
5 120 118,02 119,99
6 720 710,08 719,94
7 5 040 4 980,4 5 039,7
8 40 320 39 902,4 40 318,1
9 362 880 359 536,9 362 866,0
10 3 628 800 3 598 696 3 628 685
15 1 307 674 368 000 1,300 431 × 1,307 665 ×
20 2 432 902 008 176 640 000 2,422 787 × 2,432 882 ×
25 15 511 210 043 330 985 984 000 000 1,545 959 × 1,551 113 ×
30 265 252 859 812 191 058 636 308 480 000 000 2,645 171 × 2,652 519 ×
40 815 915 283 247 897 734 345 611 269 596 115 894 272 000 000 000 8,142 173 × 8,159 136 ×

Amawal

  • Timzgit = constante
  • Ilaw = reel
  • Amizzwr = ordre
  • Tafllawt = resultat

Iɣbula

( en ) ( fr ) Tẓḍarm ad tafim amgrad ad ɣ Wikipidya tafransist (Formule de Stirling) d Wikipidya tanglizt (Stirling's approximation) rad gisn tafim uggar n ɣaylli yad illan ɣid.