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1. The complete solution of the equationd 2 y /dx 2 + 1/x ·dy /dx ‒ (1+n 2 /x 2 )y = 0 May be writteny = AIn (x )+BKn (x ), where In (x ) = ∑r =∞ r =0(1/2x )n +2r / II (r ). II (n +r )  (1) ;

proceedings of the royal society of london

On the numerical computation of the functions G 0 ( x ), G 1 ( x ), and J n ( x √¯ i )