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  2. Reciprocal rule - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_rule

    In calculus, the reciprocal rule gives the derivative of the reciprocal of a function f in terms of the derivative of f. The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents.

  3. List of sums of reciprocals - Wikipedia

    en.wikipedia.org/wiki/List_of_sums_of_reciprocals

    The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals. The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m 2, b = mn + n 2, c = mn.

  4. Reciprocity law - Wikipedia

    en.wikipedia.org/wiki/Reciprocity_law

    In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials () with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irreducible polynomial f ( x ) = x 2 + a x + b {\displaystyle f(x)=x^{2}+ax+b} splits into linear terms ...

  5. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value

  6. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

  7. Reciprocals of primes - Wikipedia

    en.wikipedia.org/wiki/Reciprocals_of_primes

    Rules for calculating the periods of repeating decimals from rational fractions were given by James Whitbread Lee Glaisher in 1878. [5] For a prime p, the period of its reciprocal divides p − 1. [6] The sequence of recurrence periods of the reciprocal primes (sequence A002371 in the OEIS) appears in the 1973 Handbook of Integer Sequences.