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1: 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. Similarly the 6 j symbol (34.4.1) vanishes when the triangle conditions are not satisfied by any of the four 3 j symbols in the summation. …However, the 3 j and 6 j symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled. …
2: 32.4 Isomonodromy Problems
§32.4(i) Definition
(32.4.3) is the compatibility condition of (32.4.1). … … The compatibility condition of (32.4.1) with …
3: 26.11 Integer Partitions: Compositions
c ( n ) denotes the number of compositions of n , and c m ( n ) is the number of compositions into exactly m parts. …
26.11.1 c ( 0 ) = c ( T , 0 ) = 1 .
26.11.6 c ( T , n ) = F n - 1 , n 1 .
4: 26.10 Integer Partitions: Other Restrictions
26.10.1 p ( 𝒟 , 0 ) = p ( 𝒟 k , 0 ) = p ( S , 0 ) = 1 .
Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from A j , k .
p ( 𝒟 , n ) p ( 𝒟 2 , n ) p ( 𝒟 2 , T , n ) p ( 𝒟 3 , n )
26.10.6 p ( 𝒟 , n ) = 1 n t = 1 n p ( 𝒟 , n - t ) j | t j  odd j ,
26.10.7 ( - 1 ) k p ( 𝒟 , n - 1 2 ( 3 k 2 ± k ) ) = { ( - 1 ) r , n = 3 r 2 ± r , 0 , otherwise ,
26.10.12 p ( 𝒟 , n ) = p ( 𝒪 , n ) ,
5: 3.2 Linear Algebra
§3.2(iii) Condition of Linear Systems
The sensitivity of the solution vector x in (3.2.1) to small perturbations in the matrix A and the vector b is measured by the condition number …The larger the value κ ( A ) , the more ill-conditioned the system. …
§3.2(v) Condition of Eigenvalues
If A is nondefective and λ is a simple zero of p n ( λ ) , then the sensitivity of λ to small perturbations in the matrix A is measured by the condition number
6: Bibliography Y
  • A. J. Yee (2004) Partitions with difference conditions and Alder’s conjecture. Proc. Natl. Acad. Sci. USA 101 (47), pp. 16417–16418.
  • 7: 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: …
    8: 34.2 Definition: 3 j Symbol
    They therefore satisfy the triangle conditionsIf either of the conditions (34.2.1) or (34.2.3) is not satisfied, then the 3 j symbol is zero. When both conditions are satisfied the 3 j symbol can be expressed as the finite sum …
    9: 14.13 Trigonometric Expansions
    with conditional convergence for each. …
    10: 32.5 Integral Equations
    satisfies P II  with α = 0 and the boundary condition