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Partial recursive function

Partial recursive function

 are turing computable. It means that there exist a turing machine TM for every partial recursive function.

 Recursion: A function which calls itself directly or indirectly and terminates after finite number of steps is known as recursive function.

 In recursive functions,terminating point is known as base point.

 A function is called partial recursive if it is defined for some of its arguments. 
Let   f(a1,a2,....,an) is a function and defined on function     g(b1,b2,....,bm) , then f is a partial function if some elements of     f  is assigned to almost one element of function   g.

 A partial function is recursive if
i)It is an initial function over N, or
ii)It is obtained by applying recursion or composition or minimalization on initial function over N.

 'N' Natural numbers  {0,1,2,....}

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