1—10 of 178 matching pages
1: 23.13 Zeros
2: 34.10 Zeros
§34.10 Zeros►In a symbol, if the three angular momenta do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the symbol is zero. …Such zeros are called trivial zeros. …Such zeros are called nontrivial zeros. ►For further information, including examples of nontrivial zeros and extensions to symbols, see Srinivasa Rao and Rajeswari (1993, pp. 133–215, 294–295, 299–310).
3: 10.58 Zeros
§10.58 Zeros►For the th positive zeros of , , , and are denoted by , , , and , respectively, except that for we count as the first zero of . … ►
4: 9.9 Zeros
§9.9 Zeros… ►They are denoted by , , , , respectively, arranged in ascending order of absolute value for … ►
§9.9(ii) Relation to Modulus and Phase… ►
§9.9(iv) Asymptotic Expansions… ►
5: 13.22 Zeros
§13.22 Zeros… ►Asymptotic approximations to the zeros when the parameters and/or are large can be found by reversion of the uniform approximations provided in §§13.20 and 13.21. For example, if is fixed and is large, then the th positive zero of is given by …where is the th positive zero of the Bessel function (§10.21(i)). …
6: 6.13 Zeros
§6.13 Zeros►The function has one real zero , given by ►
6.13.1► and each have an infinite number of positive real zeros, which are denoted by , , respectively, arranged in ascending order of absolute value for . Values of and to 30D are given by MacLeod (1996b). …
7: 16.9 Zeros
§16.9 Zeros… ►Then has at most finitely many zeros if and only if the can be re-indexed for in such a way that is a nonnegative integer. … ►Then has at most finitely many real zeros. … ►For further information on zeros see Hille (1929).
8: 10.42 Zeros
§10.42 Zeros… ►For example, if is real, then the zeros of are all complex unless for some positive integer , in which event has two real zeros. … ►The zeros in the sector are their conjugates. … ►For -zeros of , with complex , see Ferreira and Sesma (2008). … ►
9: 8.13 Zeros
§8.13 Zeros… ►
one negative zero and no positive zeros when ;
zeros at when .