Familias Clásicas de Polinomios Ortogonales

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3VyNyV7 ]NV7y]V7
*e _!NyW!y!7 !iq!p!WVNe7
_Bj$tB8$BR I‚ N‚‚tI„‚ hz w?D
*‚ht${$?
Bt
NBR }Bj$tB8$BR I‚ N‚‚tI„‚ RBt B„BBtsj‚R ‚t >d, LdH „‚R}‚{B I‚ js PZt{$?
Bt w?D ) d k R‚ I‚ht‚t {B8BU
Qz r
Q?z
Ns PZt{$?
Bt rw?D ‚R js RBjZ{$?
Bt I‚j R$Z$‚t‚ }„BAj‚8s I‚ {BtB„tBU
hz w?D )
Q1zLd r
) (
Q?1zLd
rwdD ) r I wdD ) 3 3 3 ) r zdD wdD ) (
rwLdD ) r I wLdD ) 3 3 3 ) rzdD wLdD ) (
‚R I‚{$„ rw?D ) >w?1 dDz Ns {BtRst‚ > R‚ ‚j$‚ s„A$„s„$s8‚t‚ > ) zd 1 z
3?
B„8Zjs I‚ „‚{Z„„‚t{$s I‚ ‚t‚„s{$?
Bt I‚ js Ps8$j$s I‚ }Bj$tB8$BR
hz w?D )
1z d
zd
?hzd w?D hz1 w?D
z
z
h( w?D ) d
hd w?D ) ?
_Bj$tB8$BR I‚ NsZ‚„„‚ Uz w?D
*‚ht${$?
Bt
NBR }Bj$tB8$BR I‚ NsZ‚„„‚ RBt B„BBtsj‚R ‚t >(, L
D „‚R}‚{B I‚ js PZt{$?
Bt w?D ) ? k R‚ I‚ht‚t {B8BU
Qz r
Q?z
Ns PZt{$?
Bt rw?D ‚R js RBjZ{$?
Bt I‚j R$Z$‚t‚ }„BAj‚8s I‚ {BtB„tBU
W
z
Ld w
z
Q
?Q r
I
zdD w(D ) ( rwL D ) r I wL D ) 3 3 3 ) rzdD wL D ) (
z
Ld Q?z ) ( rw(D ) r w(D ) 3 3 3 ) r
Q?
Uz w?D ) ?
‚R I‚{$„ rw?D ) > ? ?z Ns {BtRst‚ > R‚ ‚j$‚ s„A$„s„$s8‚t‚ > ) d
3?
B„8Zjs I‚ „‚{Z„„‚t{$s I‚ ‚t‚„s{$?
Bt I‚ js Ps8$j$s I‚ }Bj$tB8$BR
Uz w?D ) w1z d ?DUzd w?D wz dD1 Uz1 w?D
U( w?D ) d
Ud w?D ) d ?
_Bj$tB8$BR I‚ <‚„8$‚ Iz w?D
*‚ht${$?
Bt
NBR }Bj$tB8$BR I‚ <‚„8$‚ RBt B„BBtsj‚R ‚t w
,L
D „‚R}‚{B I‚ js PZt{$?
Bt w?D ) ? k R‚ I‚ht‚t {B8BU
3
Qz r
Q?z
Ns PZt{$?
Bt rw?D ‚R js RBjZ{$?
Bt I‚j R$Z$‚t‚ }„BAj‚8s I‚ {BtB„tBU
z
Ld w 3 z W
Q r
Q
I
zdD w D ) (
? Q?
z ) ( rw D ) r w D ) 3 3 3 ) r
Q?zLd
3
Iz w?D ) ?
rwL
D ) rI wL
D ) 3 3 3 ) r zdD wL
D)(
‚R I‚{$„ rw?D ) > ? Ns {BtRst‚ > R‚ ‚j$‚ s„A$„s„$s8‚t‚ > ) wdDz 3
3?
B„8Zjs I‚ „‚{Z„„‚t{$s I‚ ‚t‚„s{$?
Bt I‚ js Ps8$j$s I‚ }Bj$tB8$BR
Iz w?D ) 1?Izd w?D 1wz dDIz1 w?D
I( w?D ) d
Id w?D ) 1?
_Bj$tB8$BR I‚ q{Y‚AkRY‚% xz w?D
*‚ht${$?
Bt
NBR }Bj$tB8$BR I‚ q{Y‚AkRY‚% RBt B„BBtsj‚R ‚t >d, LdH „‚R}‚{B I‚ js PZt{$?
Bt w?D ) 0 d
k R‚ I‚ht‚t {B8BU
d ?1
xz w?D ) {BRwz s„{{BR ?D
3?
B„8Zjs I‚ „‚{Z„„‚t{$s I‚ ‚t‚„s{$?
Bt I‚ js Ps8$j$s I‚ }Bj$tB8$BR
xz w?D ) 1?xzd w?D xz1 w?D
x( w?D ) d
xd w?D ) ?