Taylorren serie

1. Mat.

a zentroko ingurune batean infinitu aldiz diferentziagarria den funtzio bati dagokion berretura-seriea, non n mailako berreturaren koefizientea funtzioaren a zentroko n ordenako deribatuaren bidez kalkulatzen baita:
f(a)=f'(a)(xa) f''(a) 2! (xa) 2 +...+ f (n) (a) n! (xa) n +... MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWGHbGaaiykaiabg2da9iaadAgacaGGNaGaaiikaiaadggacaGGPaGaaiikaiaadIhacqGHsislcaWGHbGaaiykaiabgkHiTmaalaaabaGaamOzaiaacEcacaGGNaGaaiikaiaadggacaGGPaaabaGaaGOmaiaacgcaaaGaaiikaiaadIhacqGHsislcaWGHbGaaiykamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaac6cacaGGUaGaaiOlaiabgUcaRmaalaaabaGaamOzamaaCaaaleqabaGaaiikaiaad6gacaGGPaaaaOGaaiikaiaadggacaGGPaaabaGaamOBaiaacgcaaaGaaiikaiaadIhacqGHsislcaWGHbGaaiykamaaCaaaleqabaGaamOBaaaakiabgUcaRiaac6cacaGGUaGaaiOlaaaa@618F@ .
Modu laburtuan, honela adierazten da:
f(a)= n=0 f (n) (a) n! (xa) n MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWGHbGaaiykaiabg2da9maaqahabaWaaSaaaeaacaWGMbWaaWbaaSqabeaacaGGOaGaamOBaiaacMcaaaGccaGGOaGaamyyaiaacMcaaeaacaWGUbGaaiyiaaaaaSqaaiaad6gacqGH9aqpcaaIWaaabaGaeyOhIukaniabggHiLdGccaGGOaGaamiEaiabgkHiTiaadggacaGGPaWaaWbaaSqabeaacaWGUbaaaaaa@4D2B@ .