Mathematical Research Data Initiative
Main page
Recent changes
Random page
SPARQL
MaRDI@GitHub
Special pages
In other projects
MaRDI portal item
Discussion
View source
View history
Purge
English
Log in
DLMF:18.9.E6
From MaRDI portal
Formula:6299
Jump to:
navigation
,
search
MaRDI QID
Q6299
Label: DLMF:18.9.E6
Digital Library of Mathematical Functions ID
18.9.E6
(
n
+
1
2
α
+
1
2
β
+
1
)
(
1
+
x
)
P
n
(
α
,
β
+
1
)
(
x
)
=
(
n
+
1
)
P
n
+
1
(
α
,
β
)
(
x
)
+
(
n
+
β
+
1
)
P
n
(
α
,
β
)
(
x
)
,
𝑛
1
2
𝛼
1
2
𝛽
1
1
𝑥
Jacobi-polynomial-P
𝛼
𝛽
1
𝑛
𝑥
𝑛
1
Jacobi-polynomial-P
𝛼
𝛽
𝑛
1
𝑥
𝑛
𝛽
1
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
{\displaystyle{\displaystyle(n+\tfrac{1}{2}\alpha+\tfrac{1}{2}\beta+1)(1+x)P^{% (\alpha,\beta+1)}_{n}\left(x\right)=(n+1)P^{(\alpha,\beta)}_{n+1}\left(x\right% )+(n+\beta+1)P^{(\alpha,\beta)}_{n}\left(x\right),}}
Constraint(s)
Symbols List
P
n
(
α
,
β
)
(
x
)
Jacobi-polynomial-P
𝛼
𝛽
𝑛
𝑥
{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
: Jacobi polynomial
n
𝑛
{\displaystyle{\displaystyle n}}
: nonnegative integer
x
𝑥
{\displaystyle{\displaystyle x}}
: real variable
Resources that cite this formula
No records found.
Tools
What links here
Related changes
Printable version
Permanent link
Page information
