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Comparison theorems for the $\nu$-zeroes of Legendre functions $P\sp m\sb \nu(z\sb 0)$ when $-1<z\sb 0<1$
1991
Proceedings of the American Mathematical Society
We consider the problem of ordering the elements of {¡/,m(z0)} , the set of i/-zeroes of Legendre functions P™(z0) for m = 0,1,... and z0 e (-1, 1). In general, we seek to determine conditions on (m, j) and («, i) under which we can assert that vf < v" . A number of such results were established in [2] for z0 e [0, 1), and in the work that we present here we extend a number of these to the case z0 6 (-1, 1). In addition, we prove v)\x < vf+2 for z0 € (-1, 0) and v\ < v\ for z0 € (-1, 1). Using
doi:10.1090/s0002-9939-1991-1043402-x
fatcat:3kst455nfvebda5xlhxj3xz5ni