# User defined recursion – not limited

## Case 1: Fibonacci numbers using user defined recursive function

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Function fib = new Function("fib(n) = if( n>1, fib(n-1)+fib(n-2), if(n>0, 1, 0) )");

Expression e = new Expression("fib(10)", fib);

mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Res 2: fib(11) = " + fib.calculate(11));

[mXparser-v.5.2.1] Res 1: fib(10) = 55.0
[mXparser-v.5.2.1] Res 2: fib(11) = 89.0


## Case 2: Number of recursive parameters is not limited – binomial coefficient definition using user defined recursive function

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Function Cnk = new Function("Cnk(n,k) = if( k>0, if( k<n, Cnk(n-1,k-1)+Cnk(n-1,k), 1), 1)");

Expression e = new Expression("Cnk(10,3) - C(10,3)", Cnk);

mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Res 2: Cnk(10,3) = " + Cnk.calculate(10,3));

[mXparser-v.5.2.1] Res 1: Cnk(10,3) - C(10,3) = 0.0
[mXparser-v.5.2.1] Res 2: Cnk(10,3) = 120.0


## Case 3: Mixing function parameters – part causing recursive calls, other part as ‘typical’ parameter. Below example is presenting definition of Chebyshev polynomial using recursive function

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Function T = new Function("T(n,x) = if(n>1, 2*x*T(n-1,x)-T(n-2,x), if(n>0, x, 1) )");

Argument k = new Argument("k = 5");
Argument x = new Argument("x = 2");

Expression e = new Expression("T(k,x) - ( (x + sqrt(x^2-1))^k + (x - sqrt(x^2-1))^k)/2", T, k, x);
mXparser.consolePrintln("Res : " + e.getExpressionString() + " = " + e.calculate());

[mXparser-v.5.2.1] Res : T(k,x) - ( (x + sqrt(x^2-1))^k + (x - sqrt(x^2-1))^k)/2 = 0.0


## Case 4: Indirect recursion – approximating sin(x) and cos(x)

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Constant a = new Constant("a = 0.0001");

Function s = new Function("s(x) = if( abs(x) < a, x, 2*s(x/2)*c(x/2) )", a);
Function c = new Function("c(x) = if( abs(x) < a, 1, c(x/2)^2-s(x/2)^2 )", a);

/*
* Functions s and c must point to each other,
* i.e. references should be added only after
* they have been created
*/
s.addDefinitions(c);
c.addDefinitions(s);

Expression e1 = new Expression("sin(5)-s(5)", s);
Expression e2 = new Expression("cos(5)-c(5)", c);

mXparser.consolePrintln("Res 1: " + e1.getExpressionString() + " = " + e1.calculate());
mXparser.consolePrintln("Res 2: " + e2.getExpressionString() + " = " + e2.calculate());

[mXparser-v.5.2.1] Res 1: sin(5)-s(5) = 1.829204866182E-4
[mXparser-v.5.2.1] Res 2: cos(5)-c(5) = -5.410012369295E-5

###### Nuget – Package Manager

Install-Package MathParser.org-mXparser -Version 5.2.1

Nuget – .NET CLI

dotnet add package MathParser.org-mXparser --version 5.2.1

Nuget – Package Reference

<PackageReference Include="MathParser.org-mXparser" Version="5.2.1"/>

###### Maven – Dependency

<dependency><groupid>org.mariuszgromada.math</groupid><artifactid>MathParser.org-mXparser</artifactid><version>5.2.1</version></dependency>

###### Maven – Gradle

implementation 'org.mariuszgromada.math:MathParser.org-mXparser:5.2.1'

###### Maven – Gradle (Kotlin)

implementation("org.mariuszgromada.math:MathParser.org-mXparser:5.2.1")

###### GitHub

git clone https://github.com/mariuszgromada/MathParser.org-mXparser

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