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- Thread starter darida
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Sometimes it's an elegant technique to define special functions by a generating function. E.g., the Legendre Polynomials can be defined by

[tex]\frac{1}{\sqrt{r-2 r u+1}}=\sum_{l=0}^{\infty} \mathrm{P}_l(u) r^l.[/tex]

This implies that

[tex]\mathrm{P}_l(u)=\left (\frac{1}{l!} \frac{\mathrm{d}^l}{\mathrm{d} r^l} \frac{1}{\sqrt{r-2 r u+1}} \right)_{r=0}.[/tex]

Do you mean such examples?

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Chestermiller

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