# Difference between revisions of "Manuals/calci/BINOMIALSERIES"

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*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. | *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. | *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> | + | *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 | *This function will give the result as error when | ||

− | # | + | # N is not positive number. |

− | # | + | # N,X and Y is a Non-numeric. |

+ | |||

+ | ==Examples== | ||

+ | 1. BINOMIALSERIES(7,2,3) | ||

+ | |||

+ | (In the following the first term is given as 1*2^0*3^7 etc. as the binomial term) | ||

+ | |||

+ | {| class="wikitable" | ||

+ | |- | ||

+ | | 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) | ||

+ | {| class="wikitable" | ||

+ | |- | ||

+ | |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 | ||

+ | |} | ||

+ | |||

+ | ==Related Videos== | ||

+ | |||

+ | {{#ev:youtube|v=V1AKAkGJlN8|280|center|Binomial Series}} | ||

+ | |||

+ | |||

+ | ==See Also== | ||

+ | *[[Manuals/calci/BINOMIAL | BINOMIAL ]] | ||

+ | *[[Manuals/calci/BINOMIALDISTRIBUTED | BINOMIALDISTRIBUTED ]] | ||

+ | |||

+ | ==References== | ||

+ | [http://tutorial.math.lamar.edu/Classes/CalcII/BinomialSeries.aspx Binomial Series] | ||

+ | |||

+ | |||

+ | |||

+ | *[[Z_API_Functions | List of Main Z Functions]] | ||

+ | |||

+ | *[[ Z3 | Z3 home ]] |

## Latest revision as of 14:01, 10 March 2020

**BINOMIALSERIES (N,X,Y)**

- 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 and is belongs to any Complex number.
- In , is any positive integer and x and y are any real numbers.
- If k is any number and |x|<1 then,

where,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

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

## Examples

1. BINOMIALSERIES(7,2,3)

(In the following the first term is given as 1*2^0*3^7 etc. as the binomial term)

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 |

## Related Videos

## See Also

## References