查理耶多項式(Charlier polynomials)是一個以瑞典天文學家Carl Charlier命名的正交多項式,由下列拉蓋爾多項式定義[1]
前幾個查理耶多項式為
C 0 = 1 C 1 = x − 1 / m u C 2 = − x + x 2 + 2 / m u − 2 ∗ x / m u + 2 / ( ( 2 − 2 ∗ x ) ∗ m u 2 ) − 2 ∗ x / ( ( 2 − 2 ∗ x ) ∗ m u 2 ) C 3 = 2 ∗ x − 3 ∗ x 2 + x 3 − 6 / m u + 9 ∗ x / m u − 3 ∗ x 2 / m u − 12 / ( ( 2 − 2 ∗ x ) ∗ m u 2 ) + 18 ∗ x / ( ( 2 − 2 ∗ x ) ∗ m u 2 ) − 6 ∗ x 2 / ( ( 2 − 2 ∗ x ) ∗ m u 2 ) − 12 / ( ( 2 − 2 ∗ x ) ∗ ( 6 − 3 ∗ x ) ∗ m u 3 ) + 18 ∗ x / ( ( 2 − 2 ∗ x ) ∗ ( 6 − 3 ∗ x ) ∗ m u 3 ) − 6 ∗ x 2 / ( ( 2 − 2 ∗ x ) ∗ ( 6 − 3 ∗ x ) ∗ m u 3 ) {\displaystyle {\begin{aligned}C0&=1\\C1&=x-1/mu\\C2&=-x+x^{2}+2/mu-2*x/mu+2/((2-2*x)*mu^{2})-2*x/((2-2*x)*mu^{2})\\C3&=2*x-3*x^{2}+x^{3}-6/mu+9*x/mu-3*x^{2}/mu-12/((2-2*x)*mu^{2})+18*x/((2-2*x)*mu^{2})-6*x^{2}/((2-2*x)*mu^{2})-12/((2-2*x)*(6-3*x)*mu^{3})+18*x/((2-2*x)*(6-3*x)*mu^{3})-6*x^{2}/((2-2*x)*(6-3*x)*mu^{3})\\\end{aligned}}}