Looking for Errata, Gradshteyn and Ryzhik, 4th edition
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This is the edition I have as a hardcover, and even though it's old, it has served me well. Except there's quite a few errors in there and I would like to know if there's a full list available somewhere?
Note: I am using the Russian edition (1963).
There's a small list here found with Mathematica, but it's obviously incomplete.
In particular, I have found an error for 7.374(7):
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{n}^{(n-m)} (-2y^2), qquad n geq m$$
According to numerical check in Mathematica, it should be:
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{color{red}{m}}^{(n-m)} (-2y^2), qquad n geq m$$
Which is also a particular case of 7.377, which seems to be correct:
$$int_{-infty}^{infty} exp left(-x^2 right) H_m ( x+y) H_n ( x+z) dx=sqrt{pi} 2^n m! z^{n-m} L_{m}^{(n-m)} (-2yz), qquad n geq m$$
integration reference-request definite-integrals
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
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|
show 1 more comment
$begingroup$
This is the edition I have as a hardcover, and even though it's old, it has served me well. Except there's quite a few errors in there and I would like to know if there's a full list available somewhere?
Note: I am using the Russian edition (1963).
There's a small list here found with Mathematica, but it's obviously incomplete.
In particular, I have found an error for 7.374(7):
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{n}^{(n-m)} (-2y^2), qquad n geq m$$
According to numerical check in Mathematica, it should be:
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{color{red}{m}}^{(n-m)} (-2y^2), qquad n geq m$$
Which is also a particular case of 7.377, which seems to be correct:
$$int_{-infty}^{infty} exp left(-x^2 right) H_m ( x+y) H_n ( x+z) dx=sqrt{pi} 2^n m! z^{n-m} L_{m}^{(n-m)} (-2yz), qquad n geq m$$
integration reference-request definite-integrals
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
$endgroup$
3
$begingroup$
How is this not about math? I am asking for a reference to a list of errors in a world's most popular integrals tables...
$endgroup$
– Yuriy S
Dec 9 '18 at 13:18
1
$begingroup$
Concerning the English editions the errata tables are maintained by Daniel Zwillinger here.
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:29
1
$begingroup$
7.374(7) remains the same in the 8th English edition
$endgroup$
– James Arathoon
Dec 9 '18 at 13:32
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@RaymondManzoni, thank you
$endgroup$
– Yuriy S
Dec 9 '18 at 13:33
1
$begingroup$
Glad it helped @Yuriy S! You may also be interested by the proofs provided by Moll and others in this link or starting from here
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:50
|
show 1 more comment
$begingroup$
This is the edition I have as a hardcover, and even though it's old, it has served me well. Except there's quite a few errors in there and I would like to know if there's a full list available somewhere?
Note: I am using the Russian edition (1963).
There's a small list here found with Mathematica, but it's obviously incomplete.
In particular, I have found an error for 7.374(7):
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{n}^{(n-m)} (-2y^2), qquad n geq m$$
According to numerical check in Mathematica, it should be:
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{color{red}{m}}^{(n-m)} (-2y^2), qquad n geq m$$
Which is also a particular case of 7.377, which seems to be correct:
$$int_{-infty}^{infty} exp left(-x^2 right) H_m ( x+y) H_n ( x+z) dx=sqrt{pi} 2^n m! z^{n-m} L_{m}^{(n-m)} (-2yz), qquad n geq m$$
integration reference-request definite-integrals
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
$endgroup$
This is the edition I have as a hardcover, and even though it's old, it has served me well. Except there's quite a few errors in there and I would like to know if there's a full list available somewhere?
Note: I am using the Russian edition (1963).
There's a small list here found with Mathematica, but it's obviously incomplete.
In particular, I have found an error for 7.374(7):
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{n}^{(n-m)} (-2y^2), qquad n geq m$$
According to numerical check in Mathematica, it should be:
$$int_{-infty}^{infty} exp left(-(x-y)^2 right) H_m ( x) H_n ( x) dx=sqrt{pi} 2^n m! y^{n-m} L_{color{red}{m}}^{(n-m)} (-2y^2), qquad n geq m$$
Which is also a particular case of 7.377, which seems to be correct:
$$int_{-infty}^{infty} exp left(-x^2 right) H_m ( x+y) H_n ( x+z) dx=sqrt{pi} 2^n m! z^{n-m} L_{m}^{(n-m)} (-2yz), qquad n geq m$$
integration reference-request definite-integrals
integration reference-request definite-integrals
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
asked Dec 9 '18 at 13:08
Yuriy SYuriy S
15.8k433117
15.8k433117
3
$begingroup$
How is this not about math? I am asking for a reference to a list of errors in a world's most popular integrals tables...
$endgroup$
– Yuriy S
Dec 9 '18 at 13:18
1
$begingroup$
Concerning the English editions the errata tables are maintained by Daniel Zwillinger here.
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:29
1
$begingroup$
7.374(7) remains the same in the 8th English edition
$endgroup$
– James Arathoon
Dec 9 '18 at 13:32
$begingroup$
@RaymondManzoni, thank you
$endgroup$
– Yuriy S
Dec 9 '18 at 13:33
1
$begingroup$
Glad it helped @Yuriy S! You may also be interested by the proofs provided by Moll and others in this link or starting from here
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:50
|
show 1 more comment
3
$begingroup$
How is this not about math? I am asking for a reference to a list of errors in a world's most popular integrals tables...
$endgroup$
– Yuriy S
Dec 9 '18 at 13:18
1
$begingroup$
Concerning the English editions the errata tables are maintained by Daniel Zwillinger here.
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:29
1
$begingroup$
7.374(7) remains the same in the 8th English edition
$endgroup$
– James Arathoon
Dec 9 '18 at 13:32
$begingroup$
@RaymondManzoni, thank you
$endgroup$
– Yuriy S
Dec 9 '18 at 13:33
1
$begingroup$
Glad it helped @Yuriy S! You may also be interested by the proofs provided by Moll and others in this link or starting from here
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:50
3
3
$begingroup$
How is this not about math? I am asking for a reference to a list of errors in a world's most popular integrals tables...
$endgroup$
– Yuriy S
Dec 9 '18 at 13:18
$begingroup$
How is this not about math? I am asking for a reference to a list of errors in a world's most popular integrals tables...
$endgroup$
– Yuriy S
Dec 9 '18 at 13:18
1
1
$begingroup$
Concerning the English editions the errata tables are maintained by Daniel Zwillinger here.
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:29
$begingroup$
Concerning the English editions the errata tables are maintained by Daniel Zwillinger here.
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:29
1
1
$begingroup$
7.374(7) remains the same in the 8th English edition
$endgroup$
– James Arathoon
Dec 9 '18 at 13:32
$begingroup$
7.374(7) remains the same in the 8th English edition
$endgroup$
– James Arathoon
Dec 9 '18 at 13:32
$begingroup$
@RaymondManzoni, thank you
$endgroup$
– Yuriy S
Dec 9 '18 at 13:33
$begingroup$
@RaymondManzoni, thank you
$endgroup$
– Yuriy S
Dec 9 '18 at 13:33
1
1
$begingroup$
Glad it helped @Yuriy S! You may also be interested by the proofs provided by Moll and others in this link or starting from here
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:50
$begingroup$
Glad it helped @Yuriy S! You may also be interested by the proofs provided by Moll and others in this link or starting from here
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:50
|
show 1 more comment
0
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3
$begingroup$
How is this not about math? I am asking for a reference to a list of errors in a world's most popular integrals tables...
$endgroup$
– Yuriy S
Dec 9 '18 at 13:18
1
$begingroup$
Concerning the English editions the errata tables are maintained by Daniel Zwillinger here.
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:29
1
$begingroup$
7.374(7) remains the same in the 8th English edition
$endgroup$
– James Arathoon
Dec 9 '18 at 13:32
$begingroup$
@RaymondManzoni, thank you
$endgroup$
– Yuriy S
Dec 9 '18 at 13:33
1
$begingroup$
Glad it helped @Yuriy S! You may also be interested by the proofs provided by Moll and others in this link or starting from here
$endgroup$
– Raymond Manzoni
Dec 9 '18 at 13:50