On the derivatives partial derivative P-2(nu)(z)/partial derivative nu(2) and partial derivative Q(nu)(z)/partial derivative nu of the Legendre functions with respect to their degrees

摘要

We provide closed-form expressions for the degree-derivatives [partial derivative P-2(nu)(z)/partial derivative nu(2)](nu= n) and [partial derivative Q nu(z)/partial derivative nu](nu= n), with z is an element of C and n is an element of N-0, where P-nu(z) andQ(nu)(z) are the Legendre functions of the first and the second kind, respectively. For [partial derivative P-2 nu(z)/partial derivative nu(2)](nu= n), we find that