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1: 23.13 Zeros
§23.13 Zeros
For information on the zeros of ( z ) see Eichler and Zagier (1982).
2: 34.10 Zeros
§34.10 Zeros
In a 3 j symbol, if the three angular momenta j 1 , j 2 , j 3 do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the 3 j 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 9 j symbols, see Srinivasa Rao and Rajeswari (1993, pp. 133–215, 294–295, 299–310).
3: 10.58 Zeros
§10.58 Zeros
For n 0 the m th positive zeros of j n ( x ) , j n ( x ) , y n ( x ) , and y n ( x ) are denoted by a n , m , a n , m , b n , m , and b n , m , respectively, except that for n = 0 we count x = 0 as the first zero of j 0 ( x ) . …
a n , m = j n + 1 2 , m ,
b n , m = y n + 1 2 , m ,
However, there are no simple relations that connect the zeros of the derivatives. …
4: 9.9 Zeros
§9.9 Zeros
§9.9(ii) Relation to Modulus and Phase
§9.9(iv) Asymptotic Expansions
§9.9(v) Tables
Table 9.9.4: Complex zeros of Bi .
e - π i / 3 β k Bi ( β k )
5: 13.22 Zeros
§13.22 Zeros
Asymptotic approximations to the zeros when the parameters κ and/or μ are large can be found by reversion of the uniform approximations provided in §§13.20 and 13.21. For example, if μ ( 0 ) is fixed and κ ( > 0 ) is large, then the r th positive zero ϕ r of M κ , μ ( z ) is given by …where j 2 μ , r is the r th positive zero of the Bessel function J 2 μ ( x ) 10.21(i)). …
6: 6.13 Zeros
§6.13 Zeros
The function Ei ( x ) has one real zero x 0 , given by
6.13.1 x 0 = 0.37250 74107 81366 63446 19918 66580 .
Ci ( x ) and si ( x ) each have an infinite number of positive real zeros, which are denoted by c k , s k , respectively, arranged in ascending order of absolute value for k = 0 , 1 , 2 , . Values of c 1 and c 2 to 30D are given by MacLeod (1996b). …
7: 16.9 Zeros
§16.9 Zeros
Then F p p ( a ; b ; z ) has at most finitely many zeros if and only if the a j can be re-indexed for j = 1 , , p in such a way that a j - b j is a nonnegative integer. … Then F p p ( a ; b ; z ) 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 ν is real, then the zeros of I ν ( z ) are all complex unless - 2 < ν < - ( 2 - 1 ) for some positive integer , in which event I ν ( z ) has two real zeros. … The zeros in the sector - 1 2 π ph z 3 2 π are their conjugates. … For z -zeros of K ν ( z ) , with complex ν , see Ferreira and Sesma (2008). …
9: 8.13 Zeros
§8.13 Zeros
  • (a)

    one negative zero x - ( a ) and no positive zeros when 1 - 2 n < a < 2 - 2 n ;

  • As x increases the positive zeros coalesce to form a double zero at ( a n * , x n * ). The values of the first six double zeros are given to 5D in Table 8.13.1. …
    Table 8.13.1: Double zeros ( a n * , x n * ) of γ * ( a , x ) .
    n a n * x n *
    10: 14.27 Zeros
    §14.27 Zeros
    P ν μ ( x ± i 0 ) (either side of the cut) has exactly one zero in the interval ( - , - 1 ) if either of the following sets of conditions holds: …For all other values of the parameters P ν μ ( x ± i 0 ) has no zeros in the interval ( - , - 1 ) . For complex zeros of P ν μ ( z ) see Hobson (1931, §§233, 234, and 238).