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antiperiodicity

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1: 28.5 Second Solutions fe n , ge n
28.5.3 f 2 m ( z , q ) π -periodic, odd , f 2 m + 1 ( z , q ) π -antiperiodic, odd ,
28.5.4 g 2 m + 1 ( z , q ) π -antiperiodic, even , g 2 m + 2 ( z , q ) π -periodic, even ;
2: 28.3 Graphics
Even π -Antiperiodic Solutions
Odd π -Antiperiodic Solutions
3: 28.29 Definitions and Basic Properties
The π -periodic or π -antiperiodic solutions are multiples of w I ( z , λ ) , w II ( z , λ ) , respectively. …
4: 28.2 Definitions and Basic Properties
§28.2(vi) Eigenfunctions
Period π means that the eigenfunction has the property w ( z + π ) = w ( z ) , whereas antiperiod π means that w ( z + π ) = - w ( z ) . …
Table 28.2.2: Eigenfunctions of Mathieu’s equation.
Eigenvalues Eigenfunctions Periodicity Parity
a 2 n + 1 ( q ) ce 2 n + 1 ( z , q ) Antiperiod π Even
b 2 n + 1 ( q ) se 2 n + 1 ( z , q ) Antiperiod π Odd