Christoffel-Darboux formula
التعريفات والمعاني
== English ==
=== Etymology ===
Named after Elwin Bruno Christoffel and Jean Gaston Darboux.
=== Proper noun ===
the Christoffel-Darboux formula
(mathematics) An identity for a sequence of orthogonal polynomials:
∑
j
=
0
n
f
j
(
x
)
f
j
(
y
)
h
j
=
k
n
h
n
k
n
+
1
f
n
(
y
)
f
n
+
1
(
x
)
−
f
n
+
1
(
y
)
f
n
(
x
)
x
−
y
{\displaystyle \sum _{j=0}^{n}{\frac {f_{j}(x)f_{j}(y)}{h_{j}}}={\frac {k_{n}}{h_{n}k_{n+1}}}{\frac {f_{n}(y)f_{n+1}(x)-f_{n+1}(y)f_{n}(x)}{x-y}}}
where fj(x) is the jth term of a set of orthogonal polynomials of squared norm hj and leading coefficient kj.
==== Related terms ====
Christoffel-Darboux theorem