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Shivley’s matrix polynomials; Generating matrix functions; Matrix recurrence relations; summation formula; Operational representations; Euler polynomials; higher degree equations; degenerate Euler numbers and polynomials; degenerate q-Euler numbers and polynomials; degenerate Carlitz-type (p, q)-Euler numbers and polynomials; 2D q-Appell polynomials; twice-iterated 2D q-Appell polynomials; determinant expressions; recurrence relations; 2D q-Bernoulli polynomials; 2D q-Euler polynomials; 2D q-Genocchi polynomials; Apostol type Bernoulli; Euler and Genocchi polynomials; Euler numbers and polynomials; Carlitz-type degenerate (p,q)-Euler numbers and polynomials; Carlitz-type higher-order degenerate (p,q)-Euler numbers and polynomials; symmetric identities; (p, q)-cosine Bernoulli polynomials; (p, q)-sine Bernoulli polynomials; (p, q)-numbers; (p, q)-trigonometric functions; Bernstein operators; rate of approximation; Voronovskaja type asymptotic formula; q-cosine Euler polynomials; q-sine Euler polynomials; q-trigonometric function; q-exponential function; multiquadric; radial basis function; radial polynomials; the shape parameter; meshless; Kansa method