The Spherical harmonics

This is the formula used to calculate the normalization of the sperical harmonics. Using Mathmatica I just altered the value for m to recalculate the value for the l=4, m=1 to 4 terms 

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This is the formula used to calculate the Plm's for the shperical harmonics, as with the case for the normalization constants, mathematica only showed the last calucation in the printout :( 

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to calculate the Ylm's Just multiply the normilization contant by the Plm and exp(i m Phi) 

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Y40 
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******* 

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Y41 
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****** 

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Y42 
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******** 

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Y43 
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******* 

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Y44 
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*******