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Cardinal Function


The cardinal function (or Whittaker cardinal function) C(g,h,x) of g, where g:R->R is a function, with respect to an interval h>0 is, when the corresponding cardinal series of g for the interval h converges, the series

 sum_(k=-infty)^inftyg(kh)sinc((x-kh)/h),

where sinc(x) is the sinc function (McNamee et al. 1971).


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References

Gearhart, W. B. and Schulz, H. S. "The Function sinx/x." College Math. J. 21, 90-99, 1990.McNamee, J.; Stenger, F.; and Whitney, E. L. "Whittaker's Cardinal Function in Retrospect." Math. Comput. 25, 141-154, 1971.Whittaker, E. T. "On the Functions Which Are Represented by the Expansions of the Interpolation Theory." Proc. Roy. Soc. Edinburgh 35, 181-194, 1915.Whittaker, J. M. "On the Cardinal Function of Interpolation Theory." Proc. Edinburgh Math. Soc. 1, 41-46, 1927.Whittaker, J. M. Interpolary Function Theory. London, England: Cambridge University Press, 1935.

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Cardinal Function

Cite this as:

Weisstein, Eric W. "Cardinal Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CardinalFunction.html

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