Manuals/calci/BINOMIALSERIES

BINOMIALSERIES (N,X,Y)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=(1+x)^{\alpha}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} is belongs to any Complex number.
• In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle BINOMIALSERIES(N,X,Y)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} is any positive integer and x and y are any real numbers.
• If k is any number and |x|<1 then,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (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.