Manuals/calci/BINOMIALSERIES

BINOMIALSERIES (N,X,Y)

• $n_{1},n_{2},n_{3}...$ are any real numbers.

Description

• 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

1. N is not positive number.
2. N,X and Y is a Non-numeric.

Examples

1. BINOMIALSERIES(7,2,3)

1	2	0	3	7
7	2	1	3	6
21	2	2	3	5
35	2	3	3	4
35	2	4	3	3
21	2	5	3	2
7	2	6	3	1
1	2	7	3	0

2. BINOMIALSERIES(4,7,16)

1	7	0	16	4
4	7	1	16	3
6	7	2	16	2
4	7	3	16	1
1	7	4	16	0