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  2. List of trigonometric identities - Wikipedia

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

    The product-to-sum identities [28] or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems. Historically, the first four of these were known as Werner's formulas, after Johannes Werner who used them for astronomical calculations. [29]

  3. Distribution of the product of two random variables - Wikipedia

    en.wikipedia.org/wiki/Distribution_of_the...

    The product is one type of algebra for random variables: Related to the product distribution are the ratio distribution, sum distribution (see List of convolutions of probability distributions) and difference distribution. More generally, one may talk of combinations of sums, differences, products and ratios.

  4. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    Illustration of the sum formula. Draw a horizontal line (the x -axis); mark an origin O. Draw a line from O at an angle α {\displaystyle \alpha } above the horizontal line and a second line at an angle β {\displaystyle \beta } above that; the angle between the second line and the x -axis is α + β {\displaystyle \alpha +\beta } .

  5. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    7.2 Sum of reciprocal of factorials. ... Download as PDF; Printable version; In other projects ... See Faulhaber's formula.

  6. Spherical trigonometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_trigonometry

    The proof (Todhunter, [1] Art.49) of the first formula starts from the identity = ⁡, using the cosine rule to express A in terms of the sides and replacing the sum of two cosines by a product. (See sum-to-product identities.) The second formula starts from the identity = + ⁡, the third is a quotient and the remainder follow by applying the ...

  7. Convolution of probability distributions - Wikipedia

    en.wikipedia.org/wiki/Convolution_of_probability...

    The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.

  8. Proof of the Euler product formula for the Riemann zeta ...

    en.wikipedia.org/wiki/Proof_of_the_Euler_product...

    By the fundamental theorem of arithmetic, the partial product when expanded out gives a sum consisting of those terms n −s where n is a product of primes less than or equal to q. The inequality results from the fact that therefore only integers larger than q can fail to appear in this expanded out partial product.

  9. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.