Continuous Binomial Function in 3D

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This is a 3D plot of the binomial function, based on using the gamma function to extend the definition of from the integers to real numbers.

Contributed by: Larry Kealey (March 2011)
Open content licensed under CC BY-NC-SA



The controls let you set the range visible for the - plane as well as the height of the axis.

The "n-k plane plot range" slider lets you expand to . Both are expanded or contracted together.

The "z axis plot range" slider lets you expand to . As the range can be adjusted by eight orders of magnitude, it is often easier to open the control and type in the desired value.

See section 4.6, A New View of Pascal’s Triangle of [2].


[1] D. Fowler, "The Binomial Coefficient Function," American Mathematical Monthly, 103(1), 1996 pp. 1–17.

[2] S. Wagon, Mathematica in Action, New York: Springer, 2010.

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