Mixing
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Question on $sum_{pleq x}f(p)$
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In the paper of J. Barkley Rosser and Lowell Schoenfeld http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/Approximate_Formulas_for_Some_Functions_of_Prime_Numbers.pdf page 68, they obtained the following formula
My question is : should we assume that the integral 2.28 is convergent or this integral is convergent by proof?
number-theory elementary-number-theory
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
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add a comment |
$begingroup$
In the paper of J. Barkley Rosser and Lowell Schoenfeld http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/Approximate_Formulas_for_Some_Functions_of_Prime_Numbers.pdf page 68, they obtained the following formula
My question is : should we assume that the integral 2.28 is convergent or this integral is convergent by proof?
number-theory elementary-number-theory
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
$endgroup$
$begingroup$
convergence certainly depends on $f$
$endgroup$
– Hagen von Eitzen
Jan 5 at 16:14
add a comment |
$begingroup$
In the paper of J. Barkley Rosser and Lowell Schoenfeld http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/Approximate_Formulas_for_Some_Functions_of_Prime_Numbers.pdf page 68, they obtained the following formula
My question is : should we assume that the integral 2.28 is convergent or this integral is convergent by proof?
number-theory elementary-number-theory
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
$endgroup$
In the paper of J. Barkley Rosser and Lowell Schoenfeld http://www.seanerikoconnor.freeservers.com/Mathematics/AbstractAlgebra/PrimitivePolynomials/Approximate_Formulas_for_Some_Functions_of_Prime_Numbers.pdf page 68, they obtained the following formula
My question is : should we assume that the integral 2.28 is convergent or this integral is convergent by proof?
number-theory elementary-number-theory
number-theory elementary-number-theory
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
asked Jan 5 at 15:49
Theory NombreTheory Nombre
1297
1297
$begingroup$
convergence certainly depends on $f$
$endgroup$
– Hagen von Eitzen
Jan 5 at 16:14
add a comment |
$begingroup$
convergence certainly depends on $f$
$endgroup$
– Hagen von Eitzen
Jan 5 at 16:14
$begingroup$
convergence certainly depends on $f$
$endgroup$
– Hagen von Eitzen
Jan 5 at 16:14
$begingroup$
convergence certainly depends on $f$
$endgroup$
– Hagen von Eitzen
Jan 5 at 16:14
add a comment |
1 Answer
1
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$begingroup$
Your screen-shot cut off half of the explicit answer to your question (emphasis by me):
If the integral in (2.28) below con-
verges, we can rewrite (2.26) as
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
$endgroup$
$begingroup$
What does means that if the integral not converge? Is the approximation of the sum above false?
$endgroup$
– Theory Nombre
Jan 5 at 16:29
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your screen-shot cut off half of the explicit answer to your question (emphasis by me):
If the integral in (2.28) below con-
verges, we can rewrite (2.26) as
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
$endgroup$
$begingroup$
What does means that if the integral not converge? Is the approximation of the sum above false?
$endgroup$
– Theory Nombre
Jan 5 at 16:29
add a comment |
$begingroup$
Your screen-shot cut off half of the explicit answer to your question (emphasis by me):
If the integral in (2.28) below con-
verges, we can rewrite (2.26) as
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
$endgroup$
$begingroup$
What does means that if the integral not converge? Is the approximation of the sum above false?
$endgroup$
– Theory Nombre
Jan 5 at 16:29
add a comment |
$begingroup$
Your screen-shot cut off half of the explicit answer to your question (emphasis by me):
If the integral in (2.28) below con-
verges, we can rewrite (2.26) as
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
$endgroup$
Your screen-shot cut off half of the explicit answer to your question (emphasis by me):
If the integral in (2.28) below con-
verges, we can rewrite (2.26) as
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
answered Jan 5 at 16:17
Hagen von EitzenHagen von Eitzen
277k22269496
277k22269496
$begingroup$
What does means that if the integral not converge? Is the approximation of the sum above false?
$endgroup$
– Theory Nombre
Jan 5 at 16:29
add a comment |
$begingroup$
What does means that if the integral not converge? Is the approximation of the sum above false?
$endgroup$
– Theory Nombre
Jan 5 at 16:29
$begingroup$
What does means that if the integral not converge? Is the approximation of the sum above false?
$endgroup$
– Theory Nombre
Jan 5 at 16:29
$begingroup$
What does means that if the integral not converge? Is the approximation of the sum above false?
$endgroup$
– Theory Nombre
Jan 5 at 16:29
add a comment |
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$begingroup$
convergence certainly depends on $f$
$endgroup$
– Hagen von Eitzen
Jan 5 at 16:14