legendre function of second kind

2019 3 13
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更新时间：2025 4 4
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I am wondering if matlab have inbult function to compute legendre function of second kind like mathematica have LegendreQ.

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David Goodmanson
David Goodmanson 2019-3-14
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
Yashika 2019-3-14
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
Yashika 2019-3-14
It worked, thanks.
David Goodmanson
David Goodmanson 2019-3-14
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.

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回答（2 个）

Bjorn Gustavsson
Bjorn Gustavsson 2019-3-14

0 个投票

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
Sophus
Sophus 2025-4-4

0 个投票

You can use the hypergeometric function as a representation:

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