read `Cfinite.txt`:
print(`Here is a full dicovery and proof of Louis Shapiro's generating function for proudcts Chebychev polynomials of the second kind`):
print(`given in his paper   A combinatorial proof of a Chebyshev polynomial identity, Discrete Math. 34 (1981), pages 203-206.`):
KefelV(Ux(a),Ux(b)) :

print(`Here is the analogous result for Chebychev polynomials of the first kind`):

KefelV(Tx(a),Tx(b)) :

print(`And here it is for the product of the First kind times the second kind`):


KefelV(Tx(a),Ux(b)) :

print(`The three theorems and proofs took altogether`, time(), `seconds .`):

quit: