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1: 29.3 Definitions and Basic Properties
Table 29.3.1: Eigenvalues of Lamé’s equation.
eigenvalue h parity period
Table 29.3.2: Lamé functions.
boundary conditions
eigenvalue
h
eigenfunction
w ( z )
parity of
w ( z )
parity of
w ( z K )
period of
w ( z )
2: 29.12 Definitions
Table 29.12.1: Lamé polynomials.
ν
eigenvalue
h
eigenfunction
w ( z )
polynomial
form
real
period
imag.
period
parity of
w ( z )
parity of
w ( z K )
parity of
w ( z K i K )
3: 26.13 Permutations: Cycle Notation
A permutation is even or odd according to the parity of the number of transpositions. …
4: 28.2 Definitions and Basic Properties
§28.2(vi) Eigenfunctions
Even parity means w ( z ) = w ( z ) , and odd parity means w ( z ) = w ( z ) . …
Table 28.2.2: Eigenfunctions of Mathieu’s equation.
Eigenvalues Eigenfunctions Periodicity Parity
5: 1.11 Zeros of Polynomials
The number of positive zeros of a polynomial with real coefficients cannot exceed the number of times the coefficients change sign, and the two numbers have same parity. …
6: 14.30 Spherical and Spheroidal Harmonics
Parity Operation