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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
2
votes
Continuous or analytic functions with this property of sinc function
In fact, the identity is true for the function $f(x)=\frac{\sin ax}{ax}$ for each
$0\lt a\le \pi$.
For the integral part, just apply substitution.
For the series part, use the fact that $\sum_{n=1}^ …
3
votes
7
answers
1k
views
Continuous or analytic functions with this property of sinc function
This question is motivated by my previous post in SE (math.stackexchange.com).
Prove or disprove that $\frac{\sin x}{x}$ is the only nonzero entire (i.e. analytic everywhere), or continuous,
function …