Python Functions - Formula Sheet

Python Functions Reference and Syntax Sheet

Function Definition Pattern

The standard syntactic formula for creating a function in Python:

def function_name(parameter_1, parameter_2, ...):

Where:

• def: The mandatory keyword used to begin a function definition block.
• function_name: The unique identifier name of the function (following variable naming rules).
• parameter_1, parameter_2: The optional, comma-separated local variables that receive values (arguments) when called.
• return: The statement used to exit a function and optionally pass an output expression back to the caller.

Anonymous (Lambda) Function Formula

The mathematical format of a single-line lambda function:

lambda argument_list : expression

Where:

• lambda: The keyword used to define an anonymous function.
• argument_list: Comma-separated inputs passed to the function.
• expression: A single mathematical or logical operation whose calculated result is automatically returned.

Recursion Recurrence Relation (Fibonacci & Factorial Examples)

Recursive definitions can be represented as mathematical recurrence relations:

Factorial: F(n) = n * F(n-1) for n greater than 0; Base case: F(0) = 1

Fibonacci: Fib(n) = Fib(n-1) + Fib(n-2) for n greater than or equal to 2; Base cases: Fib(0) = 0, Fib(1) = 1

Where:

• n: The input parameter representing the size of the problem.
• F(n-1) / Fib(n-1): Recursive self-calls with reduced parameter sizes.
• Base case: The stopping condition that prevents infinite call stacks.

Built-in Mathematical Functions

Core mathematical relations supported by the math library:

• math.floor(x): Returns the largest integer less than or equal to x.
• math.ceil(x): Returns the smallest integer greater than or equal to x.
• math.sqrt(x): Returns the square root of x where x greater than 0.
• pow(a, b): Returns a raised to the power of b (mathematically equivalent to a**b).