Thehermitepolynomialshnxsasfythiscondionwiththeweightf

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Unformatted text preview: s
(but

 perhaps
unfamiliar)
Kronecker
delta.


It
equals
zero
if
m
and
n
are
unequal,

 and
equals
one
if
m=n.


The
former
condi=on
is
the
important
one;
the
laSer
 is
true
if
the
func=ons
are
normalized.


Note
that
the
defini=on
of
an
orthogonal
 polynomial
depends
on
not
just
the
polynomials,
but
also
the
weight
func=on
and
 a
specific
interval
of
integra=on.



 The
Hermite
polynomials
Hn(x)
sa=sfy
this
condi=on
with
the
weight
func=on
 w(x) = exp( x2 ) and
the
...
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This document was uploaded on 03/24/2014.

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