and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to...

Recursive function may refer to: Recursive function (programming), a function which references itself General recursive function, a computable partial...

Primitive recursive functions form a strict subset of those general recursive functions that are also total functions. The importance of primitive recursive functions...

function is generally simply called a function. In computability theory, a general recursive function is a partial function from the integers to the integers;...

functions and the general recursive functions. According to the Church–Turing thesis, computable functions are exactly the functions that can be calculated...

acceptable definition of a computable function defines also the same functions. General recursive functions are partial functions from integers to integers that...

recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions...

smaller instances of the same problem. Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach...

The special case of tail-recursive calls, when a function calls itself, may be more amenable to call elimination than general tail calls. When the language...

and recursive rule, one can generate the set of all natural numbers. Other recursively defined mathematical objects include factorials, functions (e.g...

Herbrand, formalized the definition of the class of general recursive functions: the smallest class of functions (with arbitrarily many arguments) that is closed...

Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions. Suppose that R(y, x1, ..., xk) is a fixed...

the general recursive definition will be given below. Let A be a set and let a0 be an element of A. If ρ is a function which assigns to each function f...

higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing...

computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input,...

operator (M operator), a function-building operator for General recursive function Möbius function, a multiplicative function in number theory and combinatorics...

defined by mathematical induction and recursive divide and conquer algorithms. Here is an example of a recursive function in C/C++ to find Fibonacci numbers:...

probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process...

recursive calls will be made (7 and 6), and the value for 5! will have been stored from the previous call. In this way, memoization allows a function...

tail call optimization in general (when the function called is not the same as the original function, as in tail-recursive calls) may be more difficult...

a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable, provable...

Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost...

while according to Robert I. Soare it is a total recursive (equivalently, general recursive) function. This article follows the second of these conventions...

Primitive recursive function General recursive function LOOP (programming language) – a programming language with the property that the functions it can...

A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce...

^{2}} ) is not an elementary recursive function. One can prove by induction that for every elementary recursive function f, there is a constant c such...

effective calculability led to a variety of proposed definitions (general recursive functions, Turing machines, λ-calculus) that later were shown to be equivalent...

36 (3): 630–636. doi:10.2307/1968646. JSTOR 1968646. 1936. "General recursive functions of natural numbers". Mathematische Annalen (112): 727–742. 1936...

arithmetic propositions involving natural numbers and any primitive recursive function, including the operations of addition, multiplication, and exponentiation...

effectively calculable function can be formalized by the general recursive functions or equivalently by the lambda-definable functions. He proves that the...