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...The legendre and associated differential equation this is an article from my home page www olewitthansen dk ole witt hansen contents series expansion solution to rodrigues formula differentiating a product n times proof of polynomials comes frequently up in physics dealing with properties solutions substantial part most standard books mathematical however are rather complex mathematics often only results presented but not detailed derivation reads d y dy x dx there two linear independent classes p q we shall here occupy ourselves called compact way state unfortunately it possible verify directly by insertion one has either use together applying binomial on or some tricks as see below especially connection replaced l fact necessary assume xa na xy xn put three terms collecting coefficients various having power since collected identically zero each certain must necessarily be messy complete task have established schema for powers const first four get...