# Polynomial Forms of SH Basis

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Hello,

I am feeling a little bit confused how polynomial forms for SH basis are presented by Robin Green and Peter-Pike Sloan.

According to Sloan Y(l=1, m=-1) = -sqrt(3) * y / sqrt(4 * PI) while Green gives the same formula but without minus sign.

The same thing for Y(l=1, m=1), Y(l=2, m=-1), etc.

I do not really buy why there is difference in minus sign for all those forms.

Thanks

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Spherical harmonics are used in linear combinations: any arbitrary sign choice for the basis functions simply flips the sign of the corresponding coefficients with no practical or theoretical consequence. Different authors might prefer different sign choices.

By the way, if you ask people to discuss specific papers rather than a general topic, you should cite your references properly with the exact title and authors and/or a download URL.

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Thank you LorenzoGatti for clarification! Yes, fair enough about the minus

Specifically, I meant then Spherical Harmonic Lighting: The Gritty Details? by Green (page 22) http://www.research.scea.com/gdc2003/spherical-harmonic-lighting.pdf

and Stupid Spherical Harmonics Tricks by Sloan (Appendix A2 Polynomial Forms of SH Basis) http://www.ppsloan.org/publications/StupidSH36.pdf

Edited by _void_

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