What is Recursive function: Definition and 29 Discussions
In mathematical logic and computer science, a general recursive function, partial recursive function, or μrecursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μrecursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μrecursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function.
Other equivalent classes of functions are the functions of lambda calculus and the functions that can be computed by Markov algorithms.
The subset of all total recursive functions with values in {0,1} is known in computational complexity theory as the complexity class R.
Here is the code that I wrote:
import numpy as np
global m, n, p, q, arr1, arr2def input():
# Input for first matrix:
print("Enter the number of rows of the first matrix: ", end="")
globals()['m'] = int(input())
print("Enter the number of columns of the first matrix: ", end="")...
Homework Statement
Find the following:
$$ \int_0^\inf \frac{x^{a+1}e^{x/\delta}}{\delta^{a+1}\Gamma(a+1)} dx; \, a > 1 , \delta >0 , 0 \leq x \leq \inf$$
Homework Equations

The Attempt at a Solution
The numerator in the integral is constant, so it can be taken outside the integral. I then...
I have been debating this issue for days:
I can't find a recursive function of this equation:
##\large{\sqrt{2+\pi \sqrt{3+\pi\sqrt{4+\pi\sqrt{5+\dotsb}}}}}##
Starting value 2 always added with pi
has been trying to find a solution this for days now, is what I have achieved so far:
This...
Homework Statement
Imagine you are playing a game with me, of drawing balls from a box. There are two blue balls and two red balls. They are picked with equal probability, and are drawn without replacement. If you draw a blue ball, I give you $1. If you draw a red ball, you pay me $1.25. What...
Homework Statement
Using these two prototypes,
double minValue( const double a[], unsigned els);
double minIndex(const double a[], unsigned els);
I am supposed to find the smallest value of an array using the minValue function as well as it's index by using the separate minIndex function and...
One way that I often write recursive functions in my work is by having an optional parameter that is used for all calls after the first. For example, here's how I might implement the classic "Find the largest palindrome in a given string" interviewtype problem:
using System;
public static...
Homework Statement
Write an iterative function char* conversion(unsigned int num, int base),
that converts an integer num into any base (base <=10).
Homework EquationsThe Attempt at a Solution
How to transform the following recursive function conversion() into iterative:
#include <stdio.h>...
Hello everyone,
Here is the problem:
Let ##\displaystyle f_0() = \frac{1}{1x}##, and ##f_n(x) = f_0(f_{n1}(x))##, where ##n \in \mathbb{N}##. Evaluate ##f_{2014}(2014)##.
I first sought after a pattern, and then tried to make a conjecture. Here is what I found:
##\displaystyle f_1(x) =...
Homework Statement
I've been asked to develop a recursive function and then analyze the asymptotic time complexity.
f(N) = 0, if N < N1
f(N1) = C1
f(N)= A1 + M1*f(M2*N/D1  S1) Op M3*f(M4*N/D2  S2), if N > N1
Homework Equations
We're to assume that:
s1 = s2 = 0
m2 =...
I have a recursive function that will eventually converge to either a fixed value or a limit cycle. Depending on the inputs, it will converge to different values (or cycles) at different rates. How could I go about measuring the rate of convergence for different inputs, regardless of what type...
Homework Statement
Hey, this isn't really homework, but my professor stated that any loop can be represented by a recursive function. Here is an example I made:
Following is a loop inside of a recursive function. I have it set up such that it takes n asterisks and prints them on a single...
Simple Recursive Function returning "nan"
Homework Statement
I have a program that is supposed to simulate a growth population. The details are not of much importance. It is a rather simple program, however, I am having problems with the program returning the final value that it has stored...
"Pure Recursive Function" for f(n) = 6n + 6n
Howdy! First of all I was going to explain a 'Pure Recursive Function' as how my professor defined it: A pure recursive function is stated by only using previous values of the function.. Like: F(n) = f(n1) + f(n2) Which means you can't have a...
Write a recursive function to compute the Jacobi symbol J(a, n), is defined for relatively prime integers a and n, a> o, \mbox{ and } n > 0 by the formula
J(a, n) = 1 \mbox{ if a = 1, } = J(a/2, n)*(1)^\frac{n^21}{8} \mbox{ if a is even, }
=J(n \% a, a)*(1)^\frac{(a1)*(n1)}{4} \mbox{...
Bonnet’s recursion formula for Legendre polynomials is
P(n,x)=1 for n=0
P(n,x)=x for n=1 and
P(n,x)= (2n1)/n*x*P(n1,x)(n1)/n*P(n2,x)
I tried to write recursive function in C to calculate the value of polynomial for a given n and x
float legpol(int n, float x)
{...
Hi,
I am having trouble understanding how this works.
I am giving the following:
y[k+2]  y[k+1] + 0.24y[k] = f[k+2]  2f[k+1];
y[2] = 1, y[1] = 2;
f[k] = 0 for k < 0;
f[k] = k for k >= 0;
I would like to have a program compute the next values in the sequence, so, I need y[2] = 1 to...
Homework Statement
Prove the correctness of the following recursive algorithm to multiply two
natural numbers, for all integer constants c ≥ 2.
function multiply(y, z)
comment Return the product yz.
1. if z = 0 then return(0) else
2. return(multiply(cy,[ z/c]) + y · (z mod c))...
Hey
i stumbled over a problem which i can't solve:
f is a continuous function on [a,b] and F_n is recursive given through:
F_1(x)=\int_a^x f(t) \ dt
and
F_{n+1}=\int_a^x F_n(t) \ dt
I have to proof that F_n looks like this:
F_n(x)=\frac{1}{(n1)!}\int_a^x (xt)^{n1} f(t) \ dt...
I have a suspicion that if f(0)=0, and f(x)=min(N\Uf(x2^i)) where i runs from 0 to i=floor(ln(x)/ln(2)), then f(x)=xmod3 for all natural numbers, x. Can anyone help me prove this inductively?
Homework Statement
Solve the recursive function:
A_{n+1} = (8/9)A_{n} + (24/9)*(20/9)^n
We want a closed formula for A_n
Homework Equations
I'm just doing this to work out the surface area of the Menger Sponge.
I know the formula's probably out there, but I get this...
can anyone help me out with this please
i want to create a recursive function in prolog to do the following thing
sum lists(X; Y;Z) holds for lists X = [x1; : : : xn], Y = [y1; : : : yn] and
Z of numbers if and only if Z = [z1; : : : zn] and zi = xi+yi (1 i n).
Hi,
I'm a beginner in C++.
I wan't to write this program:
Write a program that asks the user to enter n numbers –where n entered by the user and calculates the sum of even numbers only. main function asks the user to enter n and then calls the recursive function Sum to read the values...
Hi,
Homework Statement
Just having some troubles with a proof i have been asked to do, (sorry for not knowing the math code)
basically, f(1)=0, f(2)=1/3 and f(n)= ((n1)/(n+1))*f(n2)
and I've come up with the conjecture that f(n) = 0 when n is odd, and = 1/(n+1) when n is even...
I am trying to find a formula for f(x) = a*f(x1) + b*f(x2) for x≥1, assuming f(1) and f(0) are known. In other words, I need some expression for f(x) just in terms of a, b, f(1), and f(0).
I tried plugging in stuff and factoring on paper for the first few iterations, but it quickly got out...
I am trying to follow the book on the proof that the factorial is a primitive recursive function and it is confusing as hell. It says
0!=1 y'!=y!y' (y' means the next one so 0=0 0'=1 0''=2 etc. )
We can simply define a twoargument function with a dummy argument, and then get rid of...
Hoping someone can point out an example of a recursive function in a physics equation. If this is not a valid step that would be great to hear about too. Also if anyone has even tried to introduce such an equation in the past or how it might be represented. [I'm not the best student of maths]...
I have an assignment to write a recursive function that will safely place n Queens on an n x n chessboard. This wasn't all that difficult to figure out.
For extra credit I'm supposed to write another function(s) (recursive?) that figures out all the possible solutions. This is, so far...