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  2. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    The Pell numbers are defined by the recurrence relation: = {=; =; + In words, the sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that.

  3. Difference of two squares - Wikipedia

    en.wikipedia.org/wiki/Difference_of_two_squares

    The formula for the difference of two squares can be used for factoring polynomials that contain the square of a first quantity minus the square of a second quantity. For example, the polynomial x 4 − 1 {\displaystyle x^{4}-1} can be factored as follows:

  4. Pattern calculus - Wikipedia

    en.wikipedia.org/wiki/Pattern_calculus

    In addition, pattern calculus supports uniform access to the internal structure of arguments, be they pairs or lists or trees. Also, it allows patterns to be passed as arguments and returned as results. Uniform access is illustrated by a pattern-matching function size that computes the size of an arbitrary data structure.

  5. Differential form - Wikipedia

    en.wikipedia.org/wiki/Differential_form

    The form is pulled back to the submanifold, where the integral is defined using charts as before. For example, given a path γ(t) : [0, 1] → R 2, integrating a 1-form on the path is simply pulling back the form to a form f(t) dt on [0, 1], and this integral is the integral of the function f(t) on the interval.

  6. Arithmetic progression - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_progression

    Proof without words of the arithmetic progression formulas using a rotated copy of the blocks.. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence.

  7. Mathematics of artificial neural networks - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_artificial...

    An artificial neural network (ANN) combines biological principles with advanced statistics to solve problems in domains such as pattern recognition and game-play. ANNs adopt the basic model of neuron analogues connected to each other in a variety of ways.

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    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  9. Stars and bars (combinatorics) - Wikipedia

    en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

    For any pair of positive integers n and k, the number of k-tuples of non-negative integers whose sum is n is equal to the number of multisets of size k − 1 taken from a set of size n + 1, or equivalently, the number of multisets of size n taken from a set of size k, and is given by