NUMERICAL MATHEMATICS

Pade Approximants

ser = Series[Log[1 + x], {x, 0, 4}]

<< "Calculus`Pade`"

Information["Pade", LongForm -> True]

Pade[Normal[ser], {x, 0, 2, 2}]

NRoots[Denominator[%] == 0, x]

fun1 =  9.985  - 78.58 k  +  1015.0 k^2  - 22240.0 k^3

fun  =  
      9.948  - 57.14 k  - 875.9 k^2  + 31680.0 k^3  - 484200.0 k^4

ser  =  Series[fun,  {k, 0, 4}]

ans  =  Pade[fun,  {k, 0, 2, 2}]

NRoots[Denominator[ans] == 0, k]

NRoots[Numerator[ans] == 0, k]

Plot[ans, {k, 0, 0.1}];