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Cardinal Function


Let g:R->R be a function and let h>0, and define the cardinal series of g with respect to the interval h as the formal series

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

where sinc(x) is the sinc function. If this series converges, it is known as the cardinal function (or Whittaker cardinal function) of g, denoted C(g,h,x) (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: Cambridge University Press, 1935.

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Cardinal Function

Cite this as:

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

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