Abel polinomlari

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Matematikadagi Abel koʻphadlari koʻp nomli ketma- ketlikni hosil qiladi, uning n -chi hadi quyidagi koʻrinishga ega.








p

n


(
x
)
=
x
(
x
−
a
n

)

n
−
1


.


{\displaystyle p_{n}(x)=x(x-an)^{n-1}.}


Bu ketma-ketlik norvegiyalik kuchli matematik Niels Henrik Abel (1802-1829) sharafiga nomlangan.


Bu koʻp nomli ketma-ketlik binomial tipga ega: aksincha, binomial turdagi har bir polinom ketma-ketligini umbral hisobdagi Abel ketma-ketligidan olish ham mumkin.

Misollar

---

a = 1 uchun polinomlar








p

0


(
x
)
=
1
;


{\displaystyle p_{0}(x)=1;}







p

1


(
x
)
=
x
;


{\displaystyle p_{1}(x)=x;}







p

2


(
x
)
=
−
2
x
+

x

2


;


{\displaystyle p_{2}(x)=-2x+x^{2};}







p

3


(
x
)
=
9
x
−
6

x

2


+

x

3


;


{\displaystyle p_{3}(x)=9x-6x^{2}+x^{3};}







p

4


(
x
)
=
−
64
x
+
48

x

2


−
12

x

3


+

x

4


;


{\displaystyle p_{4}(x)=-64x+48x^{2}-12x^{3}+x^{4};}


a = 2 uchun polinomlar








p

0


(
x
)
=
1
;


{\displaystyle p_{0}(x)=1;}







p

1


(
x
)
=
x
;


{\displaystyle p_{1}(x)=x;}







p

2


(
x
)
=
−
4
x
+

x

2


;


{\displaystyle p_{2}(x)=-4x+x^{2};}







p

3


(
x
)
=
36
x
−
12

x

2


+

x

3


;


{\displaystyle p_{3}(x)=36x-12x^{2}+x^{3};}







p

4


(
x
)
=
−
512
x
+
192

x

2


−
24

x

3


+

x

4


;


{\displaystyle p_{4}(x)=-512x+192x^{2}-24x^{3}+x^{4};}







p

5


(
x
)
=
10000
x
−
4000

x

2


+
600

x

3


−
40

x

4


+

x

5


;


{\displaystyle p_{5}(x)=10000x-4000x^{2}+600x^{3}-40x^{4}+x^{5};}







p

6


(
x
)
=
−
248832
x
+
103680

x

2


−
17280

x

3


+
1440

x

4


−
60

x

5


+

x

6


;


{\displaystyle p_{6}(x)=-248832x+103680x^{2}-17280x^{3}+1440x^{4}-60x^{5}+x^{6};}

Manbalar

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Havolalar

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uz.wikipedia.org