Expressing the polynomial as a power series, , the coefficients of powers of can also be calculated using a general formula:The Legendre polynomial is determined by the values used for the two constants and , where if is odd and if is even.
ExPrESsing The PolYnomiaL As A powER seRIes, , the coeFFicientS OF pOwErs oF CAn alSo bE cAlcuLATed UsinG a generAl foRMula:thE legENdrE polynOmial is deTerminEd BY The vALues Used fOr the twO ConStaNts and , where if is OdD ANd iF iS eVen.