Question on $sum_{pleq x}f(p)$
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 2 days ago
Theory NombreTheory Nombre
1297
add a comment |
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 2 days ago
Theory NombreTheory Nombre
1297
convergence certainly depends on $f$
– Hagen von Eitzen
2 days ago
add a comment |
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 2 days ago
Theory NombreTheory Nombre
1297
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 2 days ago
Theory NombreTheory Nombre
1297
asked 2 days ago
Theory NombreTheory Nombre
1297
asked 2 days ago
Theory NombreTheory Nombre
1297
asked 2 days ago
Theory NombreTheory Nombre
1297
asked 2 days ago
Theory NombreTheory Nombre
1297
1297
convergence certainly depends on $f$
– Hagen von Eitzen
2 days ago
add a comment |
convergence certainly depends on $f$
– Hagen von Eitzen
2 days ago
convergence certainly depends on $f$
– Hagen von Eitzen
2 days ago
convergence certainly depends on $f$
– Hagen von Eitzen
2 days ago
add a comment |
1 Answer
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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 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
What does means that if the integral not converge? Is the approximation of the sum above false?
– Theory Nombre
2 days ago
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
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 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
What does means that if the integral not converge? Is the approximation of the sum above false?
– Theory Nombre
2 days ago
add a comment |
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 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
What does means that if the integral not converge? Is the approximation of the sum above false?
– Theory Nombre
2 days ago
add a comment |
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 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
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 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
answered 2 days ago
Hagen von EitzenHagen von Eitzen
276k21269496
276k21269496
What does means that if the integral not converge? Is the approximation of the sum above false?
– Theory Nombre
2 days ago
add a comment |
What does means that if the integral not converge? Is the approximation of the sum above false?
– Theory Nombre
2 days ago
What does means that if the integral not converge? Is the approximation of the sum above false?
– Theory Nombre
2 days ago
What does means that if the integral not converge? Is the approximation of the sum above false?
– Theory Nombre
2 days ago
add a comment |
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convergence certainly depends on $f$
– Hagen von Eitzen
2 days ago