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  2. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    The formula for an integration by parts is () ′ = [() ()] ′ (). Beside the boundary conditions , we notice that the first integral contains two multiplied functions, one which is integrated in the final integral ( g ′ {\displaystyle g'} becomes g {\displaystyle g} ) and one which is differentiated ( f {\displaystyle f} becomes f ...

  3. Wallace tree - Wikipedia

    en.wikipedia.org/wiki/Wallace_tree

    The final product is calculated by the weighted sum of all these partial products. The first step, as said above, is to multiply each bit of one number by each bit of the other, which is accomplished as a simple AND gate, resulting in n 2 {\displaystyle n^{2}} bits; the partial product of bits a m {\displaystyle a_{m}} by b n {\displaystyle b ...

  4. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    2.3 Product rule for multiplication by a scalar. ... Download as PDF; Printable version; ... Euler's formula; Partial fractions (Heaviside's method)

  5. 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.

  6. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    Integration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...

  7. Triple product rule - Wikipedia

    en.wikipedia.org/wiki/Triple_product_rule

    Define p 2 as the point at time t whose x-coordinate matches that of p̄ 1, and define p̄ 2 to be the corresponding point of p 2 as shown in the figure on the right. The distance Δx between p 1 and p̄ 1 is the same as the distance between p 2 and p̄ 2 (green lines), and dividing this distance by Δt yields the speed of the wave.