Complex zeros of cylinder functions

Abstract

All complex zeros of the cylinder functions Y n ( z ) , H n ( 1 ) ( z )  for  n = 0 {Y_n}(z),{H_n}^{(1)}(z){\text { for }}n = 0 and 1 1 , | z | > 158 |z| > 158 , | arg ⁡ z | ≦ π |\arg z| \leqq \pi and some complex zeros small in modulus of Y n ( z ) {Y_n}(z) , H n ( 1 ) ( z ) {H_n}^{(1)}(z) for n = 2 n = 2 , 3 3 , 4 4 , 5 5 , 15 15 and | arg ⁡ z | ≦ π |\arg z| \leqq \pi are tabulated accurate to 10 D 10D . The methods (being partly new) for computing these zeros are described.