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Integration of Functions


Many mathematical functions used in numerical computation are defined by an integral, a recurrence formula, or a series expansion.


A function in Smalltalk (the language we used for implementation) can be readily implemented with a block closure. Block closures in Smalltalk are treated like objects; thus, they can be manipulated as any other objects. For example, the one-variable function defines as

f(x) = 1 / x,

can be implemented as

f := [:x | 1 / x]

Funtion evaluation is heavily used in the area of statistics. While we did not get a chance to get involved in a mineral application applying these techniques, we believe is worth sharing with our readers the importance of its use. We do show our test implementations using Smalltalk as the language of choice.

We chose four function concepts to illustrate our handling of function evaluation: Polynomials, Error Function, Gamma Function and Beta Function.

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