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  2. Even and odd functions - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_functions

    Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose graph is self-symmetric with respect to the origin. If the domain of a real function is self-symmetric with respect to the origin, then the function can be uniquely decomposed as the sum of an even function and an ...

  3. Parity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Parity_(mathematics)

    Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That ...

  4. Odd graph - Wikipedia

    en.wikipedia.org/wiki/Odd_graph

    Although the Petersen graph has been known since 1898, its definition as an odd graph dates to the work of Kowalewski (1917), who also studied the odd graph . [2] [5] Odd graphs have been studied for their applications in chemical graph theory, in modeling the shifts of carbonium ions.

  5. Parity of a permutation - Wikipedia

    en.wikipedia.org/wiki/Parity_of_a_permutation

    If n > 1, then there are just as many even permutations in S n as there are odd ones; [3] consequently, A n contains n!/2 permutations. (The reason is that if σ is even then (1 2)σ is odd, and if σ is odd then (1 2)σ is even, and these two maps are inverse to each other.) [3] A cycle is even if and only if its length is odd. This follows ...

  6. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    (), where (2n − 1)!! is the double factorial of (2n − 1), which is the product of all odd numbers up to (2n − 1). This series diverges for every finite x , and its meaning as asymptotic expansion is that for any integer N ≥ 1 one has erfc ⁡ x = e − x 2 x π ∑ n = 0 N − 1 ( − 1 ) n ( 2 n − 1 ) ! !

  7. Constant function - Wikipedia

    en.wikipedia.org/wiki/Constant_function

    The independent variable x does not appear on the right side of the function expression and so its value is "vacuously substituted"; namely y(0) = 4, y(−2.7) = 4, y(π) = 4, and so on. No matter what value of x is input, the output is 4. [1] The graph of the constant function y = c is a horizontal line in the plane that passes through the ...