
doi: 10.5402/2012/475463
We generalize the Euler numbers and polynomials by the generalized -Euler numbers and polynomials . For the complement theorem, have interesting different properties from the Euler polynomials and we observe an interesting phenomenon of “scattering” of the zeros of the the generalized Euler polynomials in complex plane.
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), complement theorem, Euler polynomials, Binomial coefficients; factorials; \(q\)-identities, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Bernoulli and Euler numbers and polynomials
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), complement theorem, Euler polynomials, Binomial coefficients; factorials; \(q\)-identities, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.), Bernoulli and Euler numbers and polynomials
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