Certain Generalizations of Osculatory Interpolation |
Common terms and phrases
2h with given a₁ a₂ A²yo+ A4yo+ addition of multiples Ayo+ B₁ B₂ coefficients in equation cofactor contact of order curve of minimum degree 2h denominator determinant determinant for ak+r determinant is equivalent differences and second-order differences and third-order differences of yo elements fifth differences fourth-degree polynomial Institute of Actuaries interpolation curve k with curve k-i+1 determinants k+1)i+²+Mi+2 k+1)i+s+i k+I k+1 k+I k+1)² k+1 k+I k+I k+I k+r+1 k+r+i K₁ known in terms Lidstone m!am+ Mi+1 Mi+2 Mi+3 Mi+j Mi+s multiples of rows number of combinations number of terms numerator determinant order of differences osculatory interpolation formula partial-interpolation curve point h point h+1 polynomial of degree present paper r=m+I rows and columns Scott and Mathews second-order contact seventh differences sixth-degree curve slope and curvature Sprague-King successive differentiations Theorem third-order contact UNIVERSITY OF CALIFORNIA x-an x-m+n+2 x−m+n+1 y₂+i Y3+x=Yo+(x+3)Ayo+ yn+1 zero Δίνο ΣΕΣ ΣΗΣ ΣΣ ΣΣΗΣ ΣΤΗΣ