Operations on holonomic functions ================================= Addition and Multiplication --------------------------- Two holonomic functions can be added or multiplied with the result also a holonomic functions. >>> from sympy.holonomic.holonomic import HolonomicFunction, DifferentialOperators >>> from sympy.polys.domains import QQ >>> from sympy import symbols >>> x = symbols('x') >>> R, Dx = DifferentialOperators(QQ.old_poly_ring(x),'Dx') p and q here are holonomic representation of e^x and \sin(x) respectively. >>> p = HolonomicFunction(Dx - 1, x, 0, [1]) >>> q = HolonomicFunction(Dx**2 + 1, x, 0, [0, 1]) Holonomic representation of e^x+\sin(x) >>> p + q HolonomicFunction((-1) + (1)*Dx + (-1)*Dx**2 + (1)*Dx**3, x, 0, [1, 2, 1]) Holonomic representation of e^x \cdot \sin(x) >>> p * q HolonomicFunction((2) + (-2)*Dx + (1)*Dx**2, x, 0, [0, 1]) .. currentmodule:: sympy.holonomic.holonomic Integration and Differentiation ------------------------------- .. automethod:: HolonomicFunction.integrate .. automethod:: HolonomicFunction.diff Composition with polynomials ---------------------------- .. automethod:: HolonomicFunction.composition Convert to holonomic sequence ----------------------------- .. automethod:: HolonomicFunction.to_sequence Series expansion ---------------- .. automethod:: HolonomicFunction.series Numerical evaluation -------------------- .. automethod:: HolonomicFunction.evalf Convert to a linear combination of hypergeometric functions ----------------------------------------------------------- .. automethod:: HolonomicFunction.to_hyper Convert to a linear combination of Meijer G-functions ----------------------------------------------------- .. automethod:: HolonomicFunction.to_meijerg Convert to expressions ---------------------- .. automethod:: HolonomicFunction.to_expr