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Daniele Tampieri
Daniele Tampieri
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For a script I have to evaluate the associated Legendre polynomial of second kind $Q^0_{n}(z)$.

Until now, I was using an implementation that is based on the definition in equation 8.702 in the Book "Table of Integral, Series and Products" by Gradshteyn ("http://fisica.ciens.ucv.ve/~svincenz/TISPISGIMR.pdfTable of Integral, Series and Products)" by Gradshteyn.

When I insert $n=-3/2$, Matlab returns NaN, and for the term that is related to the hypergeometric function -Inf is returned. Also the book says that the expression for $Q^0_{n}(z)$ looses its meaning for $n=-3/2$. Are there other possibilities to obtain $Q^0_{-3/2}(z)$ especially for real valued $z>1$. From the expressions in Gradshteyn I expect real valued solutions however the Mathematica function LegendreQ returns complex values. Where does this come from?

Many thanks for any help

For a script I have to evaluate the associated Legendre polynomial of second kind $Q^0_{n}(z)$.

Until now, I was using an implementation that is based on the definition in equation 8.702 in the Book "Table of Integral, Series and Products" by Gradshteyn (http://fisica.ciens.ucv.ve/~svincenz/TISPISGIMR.pdf).

When I insert $n=-3/2$, Matlab returns NaN, and for the term that is related to the hypergeometric function -Inf is returned. Also the book says that the expression for $Q^0_{n}(z)$ looses its meaning for $n=-3/2$. Are there other possibilities to obtain $Q^0_{-3/2}(z)$ especially for real valued $z>1$. From the expressions in Gradshteyn I expect real valued solutions however the Mathematica function LegendreQ returns complex values. Where does this come from?

Many thanks for any help

For a script I have to evaluate the associated Legendre polynomial of second kind $Q^0_{n}(z)$.

Until now, I was using an implementation that is based on the definition in equation 8.702 in the Book "Table of Integral, Series and Products" by Gradshteyn.

When I insert $n=-3/2$, Matlab returns NaN, and for the term that is related to the hypergeometric function -Inf is returned. Also the book says that the expression for $Q^0_{n}(z)$ looses its meaning for $n=-3/2$. Are there other possibilities to obtain $Q^0_{-3/2}(z)$ especially for real valued $z>1$. From the expressions in Gradshteyn I expect real valued solutions however the Mathematica function LegendreQ returns complex values. Where does this come from?

Many thanks for any help

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BenjaminBluemchen
BenjaminBluemchen
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How are the Legendre Polynomials of second kind for negative degrees defined?

For a script I have to evaluate the associated Legendre polynomial of second kind $Q^0_{n}(z)$.

Until now, I was using an implementation that is based on the definition in equation 8.702 in the Book "Table of Integral, Series and Products" by Gradshteyn (http://fisica.ciens.ucv.ve/~svincenz/TISPISGIMR.pdf).

When I insert $n=-3/2$, Matlab returns NaN, and for the term that is related to the hypergeometric function -Inf is returned. Also the book says that the expression for $Q^0_{n}(z)$ looses its meaning for $n=-3/2$. Are there other possibilities to obtain $Q^0_{-3/2}(z)$ especially for real valued $z>1$. From the expressions in Gradshteyn I expect real valued solutions however the Mathematica function LegendreQ returns complex values. Where does this come from?

Many thanks for any help