` c=series(func,v)`

` c=series(func,v,n)`

Inputs | |

`func` |
The function of a single variable whose series is to be found. |

`v` |
The value of the variable at which the series is to be found. |

`n` |
The desired number of terms in the series. |

Outputs | |

`c` |
The vector from which the coefficients of the Taylor series may be easily computed (see below). |

The output is such that the near

`x=v`

the function can be approximated
by
` c[1]+c[2]*(x-v)+c[3]*(x-v)^2+....c[n]*(x-v)^(n-1).`

(Actual coefficients of the Taylor series are

`c[i]/factorial(i-1)`

).
Note that the series of only a limited set of functions can be computed. The
main restrictions are (a) the function be real and scalar valued, (b) all
the steps involved in the computaion must involve only the arithmetic
operators and trigonometric, exponential, hyperbolic, or logarithmic functions.
>>series(@sin,0)0 1 0 -0.1667 0>>series(@(x)sin(x^2-2x),0)4.9304e-032 -2 1 1.3333 -2>>series(@sin,0,10)Columns 1 through 8 0 1 0 -0.1667 0 0.0083 0 -0.0002 Columns 9 through 10 0 2.7557e-006>>series(@(x)sin(x^2-2x),0,10)Columns 1 through 8 4.9304e-032 -2 1 1.3333 -2 0.7333 0.5 -0.6413 Columns 9 through 10 0.2444 0.0486>>// The first term is the limit of the function sin(x)/x as x->0>>series(@(x)sin(x)/x,0)1 0 -0.1667 0