Orthogonality of generalized Newton symbol
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Consider the functions $P_{n}(x)={x choose n}.$ My question is, if there exists a measure $mu$ with support being a subset of $(0,infty)$ such that the family ${P_{n}}$ is orthogonal in $L^{2}(mu)$, i.e. $$int {x choose n}{x choose m},dmu=0$$
for $nneq m$?
combinatorics discrete-mathematics orthogonality orthogonal-polynomials
asked Nov 19 at 17:57
Isak
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up vote
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down vote
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Consider the functions $P_{n}(x)={x choose n}.$ My question is, if there exists a measure $mu$ with support being a subset of $(0,infty)$ such that the family ${P_{n}}$ is orthogonal in $L^{2}(mu)$, i.e. $$int {x choose n}{x choose m},dmu=0$$
for $nneq m$?
combinatorics discrete-mathematics orthogonality orthogonal-polynomials
asked Nov 19 at 17:57
Isak
113
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Consider the functions $P_{n}(x)={x choose n}.$ My question is, if there exists a measure $mu$ with support being a subset of $(0,infty)$ such that the family ${P_{n}}$ is orthogonal in $L^{2}(mu)$, i.e. $$int {x choose n}{x choose m},dmu=0$$
for $nneq m$?
combinatorics discrete-mathematics orthogonality orthogonal-polynomials
asked Nov 19 at 17:57
Isak
113
Consider the functions $P_{n}(x)={x choose n}.$ My question is, if there exists a measure $mu$ with support being a subset of $(0,infty)$ such that the family ${P_{n}}$ is orthogonal in $L^{2}(mu)$, i.e. $$int {x choose n}{x choose m},dmu=0$$
for $nneq m$?
combinatorics discrete-mathematics orthogonality orthogonal-polynomials
combinatorics discrete-mathematics orthogonality orthogonal-polynomials
asked Nov 19 at 17:57
Isak
113
asked Nov 19 at 17:57
Isak
113
edited Nov 19 at 20:47
asked Nov 19 at 17:57
Isak
113
asked Nov 19 at 17:57
Isak
113
asked Nov 19 at 17:57
Isak
113
113
add a comment |
add a comment |
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