zeros
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1: 23.13 Zeros
2: 34.10 Zeros
§34.10 Zeros
βΊIn 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. βΊFor 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
βΊFor the th positive zeros of , , , and are denoted by , , , and , respectively, except that for we count as the first zero of . … βΊ4: 9.9 Zeros
§9.9 Zeros
… βΊThey are denoted by , , , , respectively, arranged in ascending order of absolute value for … βΊ§9.9(ii) Relation to Modulus and Phase
… βΊ§9.9(iv) Asymptotic Expansions
… βΊ§9.9(v) Tables
…5: 13.22 Zeros
§13.22 Zeros
… βΊAsymptotic 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
βΊThe function has one real zero , given by βΊ
6.13.1
βΊ
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).
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