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**Extensions of the Sine Addition Formula on Monoids.** / Ebanks, Bruce; Stetkær, Henrik.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Ebanks, B & Stetkær, H 2018, 'Extensions of the Sine Addition Formula on Monoids', *Results in Mathematics*, vol. 73, no. 3, 119. https://doi.org/10.1007/s00025-018-0880-z

Ebanks, B., & Stetkær, H. (2018). Extensions of the Sine Addition Formula on Monoids. *Results in Mathematics*, *73*(3), [119]. https://doi.org/10.1007/s00025-018-0880-z

Ebanks B, Stetkær H. 2018. Extensions of the Sine Addition Formula on Monoids. Results in Mathematics. 73(3). https://doi.org/10.1007/s00025-018-0880-z

Ebanks, Bruce and Henrik Stetkær. "Extensions of the Sine Addition Formula on Monoids". *Results in Mathematics*. 2018. 73(3). https://doi.org/10.1007/s00025-018-0880-z

Ebanks B, Stetkær H. Extensions of the Sine Addition Formula on Monoids. Results in Mathematics. 2018 Sep 1;73(3). 119. https://doi.org/10.1007/s00025-018-0880-z

Ebanks, Bruce ; Stetkær, Henrik. / **Extensions of the Sine Addition Formula on Monoids**. In: Results in Mathematics. 2018 ; Vol. 73, No. 3.

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title = "Extensions of the Sine Addition Formula on Monoids",

abstract = "It is known that a pair (f, g) of functions with f≠ 0 satisfies the sine addition formula f(xy) = f(x) g(y) + g(x) f(y) on a semigroup only if g= (μ1+ μ2) / 2 where μ1 and μ2 are multiplicative functions. Here we solve the variant f(xy) = g1(x) h1(y) + g(x) h2(y) for four unknown functions f, g1, h1, h2 on a monoid, where g is not simply the average of two multiplicative functions but more generally a linear combination of n≥ 2 distinct multiplicative functions.",

keywords = "character, functional equation, multiplicative function, Sine addition formula, topological semigroup",

author = "Bruce Ebanks and Henrik Stetk{\ae}r",

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