legendre function of second kind

I am wondering if matlab have inbult function to compute legendre function of second kind like mathematica have LegendreQ.

[David Goodmanson]

Hi yashika,

I don't believe so, although I would be happy to be proved wrong. Meanwhile,f you are looking for the basic legendre Q function with mu = 0 (not the associated legendre functions with mu ~= 0), then if n is not too large the expression

Q_n_(x) = (1/2) P_n_(x) log((1+x)/(1-x)) - Sum{1:n} (1/m) P_m-1_(x) P_n-m_(x)

should do reasonably well.

[Yashika]

Yes I have basic legendre functions, and i need only first few functions like Q0 to Q20 , I will try this, Thank you for the help.

[Yashika]

It worked, thanks.

[David Goodmanson]

I don't know how accurate that might be for n as high as 20, and it would be interesting to see how well the recurrence relation is satisfied in the region n ~~ 20.

Answer 1

[Bjorn Gustavsson]

You can find a toolbox for special functions on the file exchange: Computation of Special Functions

I haven't (or at least don't remember) used this toolbox, but it might solve your task.

HTH

[Yashika]

Thanks, will give it a shot.

Answer 2

[Sophus]

You can use the hypergeometric function as a representation:

[David Goodmanson]

you can as long as |z| > 1, not otherwise.