Mixing
Can the series expansion of a convergent integral be divergent?
$begingroup$
This is the screenshot from Arfken and Weber.
The series expansion for the given integral diverges for all x.
If I check on a calculator, it gives $I(5,1)=0.001148$. It means the integral converges for $x=5$ and $p=1$. Similarly, the integral converges for other finite values of $x$ and $p$. But the series expansion says that the integral diverges.
The author has only used Integration by Parts. How can it make a convergent integral divergent? It doesn't seem there is any mistake in this method.
convergence gamma-function
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
$endgroup$
add a comment |
$begingroup$
This is the screenshot from Arfken and Weber.
The series expansion for the given integral diverges for all x.
If I check on a calculator, it gives $I(5,1)=0.001148$. It means the integral converges for $x=5$ and $p=1$. Similarly, the integral converges for other finite values of $x$ and $p$. But the series expansion says that the integral diverges.
The author has only used Integration by Parts. How can it make a convergent integral divergent? It doesn't seem there is any mistake in this method.
convergence gamma-function
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
$endgroup$
add a comment |
$begingroup$
This is the screenshot from Arfken and Weber.
The series expansion for the given integral diverges for all x.
If I check on a calculator, it gives $I(5,1)=0.001148$. It means the integral converges for $x=5$ and $p=1$. Similarly, the integral converges for other finite values of $x$ and $p$. But the series expansion says that the integral diverges.
The author has only used Integration by Parts. How can it make a convergent integral divergent? It doesn't seem there is any mistake in this method.
convergence gamma-function
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
$endgroup$
This is the screenshot from Arfken and Weber.
The series expansion for the given integral diverges for all x.
If I check on a calculator, it gives $I(5,1)=0.001148$. It means the integral converges for $x=5$ and $p=1$. Similarly, the integral converges for other finite values of $x$ and $p$. But the series expansion says that the integral diverges.
The author has only used Integration by Parts. How can it make a convergent integral divergent? It doesn't seem there is any mistake in this method.
convergence gamma-function
convergence gamma-function
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
asked Jan 7 at 11:31
Asit SrivastavaAsit Srivastava
257
257
add a comment |
add a comment |
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