Generalized hyperbolic functions, circulant matrices and functional equations

There is a contrast between the two sets of functional equations f 0 ( x + y ) = f 0 ( x ) f 0 ( y ) + f 1 ( x ) f 1 ( y ) , f 1 ( x + y ) = f 1 ( x ) f 0 ( y ) + f 0 ( x ) f 1 ( y ) , and f 0 ( x - y ) = f 0 ( x ) f 0 ( y ) - f 1 ( x ) f 1 ( y ) , f 1 ( x - y ) = f 1 ( x ) f 0 ( y ) - f 0 ( x ) f 1...

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