private Node GenerateMaclaurinSeriesPolynomial(double x, int order)
{
if (order == 0)
{
return(this);
}
if (order == 1)
{
return(new PlusSign(new MultiplicationSign(ReturnDerivative(x), new VariableNode()), this));
}
VariableNode variableNode = new VariableNode();
NaturalNumberNode orderNode = new NaturalNumberNode(order);
CaretSign caretSign = new CaretSign(variableNode, orderNode);
Node f0 = ReturnDerivative(x);
for (int i = 1; i < order; i++)
{
f0 = f0.ReturnDerivative(x);
}
MultiplicationSign multiplicationSign = new MultiplicationSign(caretSign, new RationalNumberNode(f0.Calculate(0)));
FactorialFunction factorialFunction = new FactorialFunction(orderNode);
DivisionSign divisionSign = new DivisionSign(multiplicationSign, factorialFunction);
return(new PlusSign(divisionSign, ReturnMaclaurinSeriesPolynomial(x, order - 1)));
}
public double ReturnMaclaurinSeries(double x, int order)
{
if (order == 0)
{
return(Calculate(0));
}
if (order == 1)
{
return(ReturnDerivative(x).Calculate(0) * x + Calculate(0));
}
VariableNode variableNode = new VariableNode();
NaturalNumberNode orderNode = new NaturalNumberNode(order);
CaretSign caretSign = new CaretSign(variableNode, orderNode);
Node f0 = ReturnDerivative(x);
for (int i = 1; i < order; i++)
{
f0 = f0.ReturnDerivative(x);
}
MultiplicationSign multiplicationSign = new MultiplicationSign(caretSign, new RationalNumberNode(f0.Calculate(0)));
FactorialFunction factorialFunction = new FactorialFunction(orderNode);
DivisionSign divisionSign = new DivisionSign(multiplicationSign, factorialFunction);
return(divisionSign.Calculate(x) + ReturnMaclaurinSeries(x, order - 1));
}
public double ReturnNewtonMaclaurinSeries(double x, int order)
{
if (order == 0)
{
return(Calculate(0));
}
if (order == 1)
{
return(ReturnNewtonDerivative(0) * x + Calculate(0));
}
VariableNode variableNode = new VariableNode();
NaturalNumberNode orderNode = new NaturalNumberNode(order);
CaretSign caretSign = new CaretSign(variableNode, orderNode);
RationalNumberNode f0 = new RationalNumberNode(CalculatePolynomialDerivative(0, order));
MultiplicationSign multiplicationSign = new MultiplicationSign(caretSign, f0);
FactorialFunction factorialFunction = new FactorialFunction(orderNode);
DivisionSign divisionSign = new DivisionSign(multiplicationSign, factorialFunction);
return(divisionSign.Calculate(x) + ReturnNewtonMaclaurinSeries(x, order - 1));
}