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Combinatorical Functions

The grapher has a built-in set of combinatorical functions specified in the list below. The combinatorical functions below are only defined for integers or natural numbers. The value of the function at point x will be calculated with floor(x) meaning that the number will be rounded to the largest number which is smaller than x. For example: fac(5.3) will be evaluted by using fac(5) or binco(4.2, 5.7) will be evaluated by using binco(4, 5). In that sense the combinatorical functions are step functions.

function name examples remarks
fac Factorial fac(x), sin(x)/cos(fac(x))
binco Binomial Coefficient binco(x, x/2), binco(x, sin(x)) the first parameter is the size of the set we want to to choose from and the second parameter is the size of the set that we are choosing e.g. binco(3, 4) = $\binom{3}{4}$. For more information see binomial coefficient
catalan Catalan Numbers catalan(x) The sequence is calculate using the formula catalan(x) = $\frac{1}{n+1}\binom{2x}{x}$
fib Fibonacci Numbers fib(x), fib(sin(x)), log(x,fib(x)), (x/log(fib(x))) The sequence is calculated using the formula fib(x) = $\frac{\varphi^x-(1-\varphi)^x}{\sqrt{5}}$. Where $\varphi$ is the golden ratio (see Function Input). For more information about this sequence see Fibonacci Number. The sequence is extended to negative numbers (see Negative Fibonacci for more information).

limitions on combinatorical functions

The functions listed above have a very high growth rate, meaning that for a relatively small input (domain) their value is very large (range). If the value of one of the function is too large, the function will no be drawn. This is also true for functions using the functions above. Each of function has its own growth rate and plotting will stop at diffrent points.