Difference between revisions of "Manuals/calci/BINOMIALSERIES"

Revision as of 14:28, 13 December 2016

BINOMIALSERIES (N,X,Y)

This function gives the coefficient of the Binomial series.
BinomialSeries is also called Maclaurin series for the function f given by $f(x)=(1+x)^{\alpha }$ and $\alpha$ is belongs to any Complex number.
In $BINOMIALSERIES(N,X,Y)$ , $N$ is any positive integer and x and y are any real numbers.
If k is any number and |x|<1 then, $(1+x)^{k}=\sum _{n=0}^{\infty }{\binom {k}{n}}x^{n}$

 where ${\binom {k}{n}}={\frac {k(k-1)(k-2)...(k-n+1)}{n!}}$ ,n=1,2,3...

So similar to the binomial theorem except that it’s an infinite series and we must have in order to get convergence.
This function will give the result as error when

@@ Line 6: / Line 6: @@
 *BinomialSeries is also called  Maclaurin series for the function  f given by <math> f(x)=(1+x)^{\alpha}</math> and <math>\alpha</math> is belongs to any Complex number.
 *In <math>BINOMIALSERIES(N,X,Y)</math>,<math>N</math> is any positive integer and x and y are any real numbers.
-*If k is any number and |x|<1 then,<math>(1+x)^k= \sum_{n=0}^\infty \binom{k}{n} x^n</math>  where<math> \binom{k}{n} = \frac{k(k-1)(k-2)...(k-n+1)}{n!} </math>,n=1,2,3...http://tutorial.math.lamar.edu/Classes/CalcII/BinomialSeries.aspx.
+*If k is any number and |x|<1 then,<math>(1+x)^k= \sum_{n=0}^\infty \binom{k}{n} x^n</math>
+  where<math> \binom{k}{n} = \frac{k(k-1)(k-2)...(k-n+1)}{n!} </math>,n=1,2,3...
 *So  similar to the binomial theorem except that it’s an infinite series and we must have  in order to get convergence.
 *This function will give the result as error when
 #1. N is not positive number.
 #2. N,X and Y is a Non-numeric.