Cardinal Function

Let  be a function and let , and define the cardinal series of  with respect to the interval  as the formal series

where  is the sinc function. If this series converges, it is known as the cardinal function (or Whittaker cardinal function) of , denoted  (McNamee et al. 1971).

REFERENCES:

Gearhart, W. B. and Schulz, H. S. "The Function ." 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.