Everett interpolation | Laplace-Everett formula

f_p = (1 - p) f_0 + p f_1 + E_2 δ_0^2 + F_2 δ_1^2 + E_4 δ_0^4 + F_4 δ_1^4 + E_6 δ_0^6 + F_6 δ_1^6 + ..., for p element [0, 1], where δ is the central difference and E_(2n) | congruent | G_(2n) - G_(2n + 1) | congruent | B_(2n) - B_(2n + 1) F_(2n) | congruent | G_(2n + 1) | congruent | B_(2n) + B_(2n + 1), where G_k are the coefficients from Gauss's backward formula and Gauss's forward formula and B_k are the coefficients from Bessel's finite difference formula.