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Manuals/calci/PASCALTRIANGLE
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Revision as of 07:57, 22 January 2014
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07:57, 22 January 2014
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==Description==
==Description==
*This function gives the Coefficients of the Pascal triangle.
*This function gives the Coefficients of the Pascal triangle.
−
*In <math>PASCALTRIANGLE(r)</math> , r is the row number of the Pascal triangle.
+
*In <math>PASCALTRIANGLE(r)</math> ,
<math>
r
</math>
is the row number of the Pascal triangle.
*Pascal triangle is the arrangement of numbers of the Binomial coefficients in a triangular shape.
*Pascal triangle is the arrangement of numbers of the Binomial coefficients in a triangular shape.
−
*It is started with the number 1 at the top in the 1st row.
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*It is started with the number
<math>
1
</math>
at the top in the 1st row.
*Then from the 2nd row each number in the triangle is the sum of the two directly above it.
*Then from the 2nd row each number in the triangle is the sum of the two directly above it.
−
*The construction is related to the
binomial coefficients
by Pascal's rule is :
+
*The construction is related to the
Binomial Coefficients
by Pascal's rule is :
−
<math>(x+y)^n=\sum_{k=0}^n \binom{n}{k}x^{n-k} .y^k </math>.
where <math> \dbinom{n}{k}</math> is the binomial coefficient.
+
<math>(x+y)^n=\sum_{k=0}^n \binom{n}{k}x^{n-k} .y^k </math>.
+
where <math> \dbinom{n}{k}</math> is the binomial coefficient.
*This function will return the result as error when <math> r \le 0</math>.
*This function will return the result as error when <math> r \le 0</math>.
Abin
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