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Roughness of $intsqrt{1-t^2}f(t),dt$ in $[-1,1]$

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0

1

$begingroup$

Why is this integrand non-smooth in $[-1,1]$?
$$intsqrt{1-t^2}f(t),dt$$
where $f$ possesses an analytic extinction to a complex neighbourhood $[-1,1]$

More general, how can I find it out?

Thanks a lot!

real-analysis integration definite-integrals quadrature

share|cite|improve this question

edited Mar 12 at 3:08

Parcly Taxel

44.6k1376109

asked Jan 20 at 13:40

scalpulascalpula

175

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If $fequiv 0$ the the integral is smooth.
  $endgroup$
  – Kavi Rama Murthy
  Mar 12 at 5:53
  

  
  
  
  

add a comment | 

0

1

$begingroup$

Why is this integrand non-smooth in $[-1,1]$?
$$intsqrt{1-t^2}f(t),dt$$
where $f$ possesses an analytic extinction to a complex neighbourhood $[-1,1]$

More general, how can I find it out?

Thanks a lot!

real-analysis integration definite-integrals quadrature

share|cite|improve this question

edited Mar 12 at 3:08

Parcly Taxel

44.6k1376109

asked Jan 20 at 13:40

scalpulascalpula

175

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If $fequiv 0$ the the integral is smooth.
  $endgroup$
  – Kavi Rama Murthy
  Mar 12 at 5:53
  

  
  
  
  

add a comment | 

$begingroup$

Why is this integrand non-smooth in $[-1,1]$?
$$intsqrt{1-t^2}f(t),dt$$
where $f$ possesses an analytic extinction to a complex neighbourhood $[-1,1]$

More general, how can I find it out?

Thanks a lot!

real-analysis integration definite-integrals quadrature

share|cite|improve this question

edited Mar 12 at 3:08

Parcly Taxel

44.6k1376109

asked Jan 20 at 13:40

scalpulascalpula

175

$endgroup$

share|cite|improve this question

edited Mar 12 at 3:08

Parcly Taxel

44.6k1376109

asked Jan 20 at 13:40

scalpulascalpula

175

share|cite|improve this question

edited Mar 12 at 3:08

Parcly Taxel

44.6k1376109

asked Jan 20 at 13:40

scalpulascalpula

175

edited Mar 12 at 3:08

Parcly Taxel

44.6k1376109

edited Mar 12 at 3:08

Parcly Taxel

44.6k1376109

asked Jan 20 at 13:40

scalpulascalpula

175

asked Jan 20 at 13:40

scalpulascalpula

175