Series expansion with bounded coefficients Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Taylor / Maclaurin series expansion origin.how do you determine what the coefficients are on a taylor series expansion if the derivative is too hard to compute?Taylor expansion of $1/(1+z)$Taylor series expansion of multiple termsSeries expansion of $arctan$ at arbitrary real pointCoefficients of power series involving binomial expansionExpansion in power series of $z=0$Coefficients of the stirling's series expansion for the factorial.Series expansion of $left(1 + x^2right)^-1/2$Maclaurin's series for $cossqrtx$
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Series expansion with bounded coefficients
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Taylor / Maclaurin series expansion origin.how do you determine what the coefficients are on a taylor series expansion if the derivative is too hard to compute?Taylor expansion of $1/(1+z)$Taylor series expansion of multiple termsSeries expansion of $arctan$ at arbitrary real pointCoefficients of power series involving binomial expansionExpansion in power series of $z=0$Coefficients of the stirling's series expansion for the factorial.Series expansion of $left(1 + x^2right)^-1/2$Maclaurin's series for $cossqrtx$
$begingroup$
Consider the two variable function $$f(x,y)=sqrtx^2+y^2.$$ The function is continuous and therefore bounded on compact sets. We may expand the function as the following series using binomial series:
$$f(x,y)=x+fracy2-fracy^28x+fracy^316x^2-cdots$$
Why is it that, even though, the function is bounded, the coefficients of the power series are unbounded in $x$? I guess this is due to the loss of differentiability at $(0,0)$. Is it possible to obtain a power series expansion for $f$ with bounded coefficients?
real-analysis power-series taylor-expansion
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
$endgroup$
add a comment |
$begingroup$
Consider the two variable function $$f(x,y)=sqrtx^2+y^2.$$ The function is continuous and therefore bounded on compact sets. We may expand the function as the following series using binomial series:
$$f(x,y)=x+fracy2-fracy^28x+fracy^316x^2-cdots$$
Why is it that, even though, the function is bounded, the coefficients of the power series are unbounded in $x$? I guess this is due to the loss of differentiability at $(0,0)$. Is it possible to obtain a power series expansion for $f$ with bounded coefficients?
real-analysis power-series taylor-expansion
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
$endgroup$
add a comment |
$begingroup$
Consider the two variable function $$f(x,y)=sqrtx^2+y^2.$$ The function is continuous and therefore bounded on compact sets. We may expand the function as the following series using binomial series:
$$f(x,y)=x+fracy2-fracy^28x+fracy^316x^2-cdots$$
Why is it that, even though, the function is bounded, the coefficients of the power series are unbounded in $x$? I guess this is due to the loss of differentiability at $(0,0)$. Is it possible to obtain a power series expansion for $f$ with bounded coefficients?
real-analysis power-series taylor-expansion
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
$endgroup$
Consider the two variable function $$f(x,y)=sqrtx^2+y^2.$$ The function is continuous and therefore bounded on compact sets. We may expand the function as the following series using binomial series:
$$f(x,y)=x+fracy2-fracy^28x+fracy^316x^2-cdots$$
Why is it that, even though, the function is bounded, the coefficients of the power series are unbounded in $x$? I guess this is due to the loss of differentiability at $(0,0)$. Is it possible to obtain a power series expansion for $f$ with bounded coefficients?
real-analysis power-series taylor-expansion
real-analysis power-series taylor-expansion
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
edited Apr 2 at 15:59
Tanuj Dipshikha
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
asked Apr 2 at 14:28
Tanuj DipshikhaTanuj Dipshikha
304310
304310
add a comment |
add a comment |
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