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  2. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    Since the function cosh x is even, only even exponents for x occur in its Taylor series. The sum of the sinh and cosh series is the infinite series expression of the exponential function. The following series are followed by a description of a subset of their domain of convergence, where the series is convergent and its sum equals the function.

  3. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    for the definition of the principal values of the inverse hyperbolic tangent and cotangent. In these formulas, the argument of the logarithm is real if and only if z is real. For artanh, this argument is in the real interval (−∞, 0] , if z belongs either to (−∞, −1] or to [1, ∞) .

  4. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.

  5. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

  6. Cosh - Wikipedia

    en.wikipedia.org/wiki/Cosh

    cosh (mathematical function), hyperbolic cosine, a mathematical function with notation cosh(x)-COSH, a representation of the thiocarboxylic acid functional group in chemistry; Chlorpromazine, an antipsychotic drug; ChromeOS Shell, an operating system designed by Google

  7. Biden slammed for commuting sentence of notorious ‘Kids-for ...

    www.aol.com/news/biden-slammed-commuting...

    Ex-Judge Michael Conahan, the jurist at the center of the so-called “Kids-for-Cash” scandal, was among 1,499 commutations Biden granted in the largest presidential act of clemency on a single day.

  8. 'Biden got it absolutely wrong': Pa. officials condemn ...

    www.aol.com/biden-got-absolutely-wrong-pa...

    Kids for cash victim Amanda Lorah also decried the commutation. "It’s a big slap in the face for us once again,” Lorah told WBRE-TV news in Wilkes-Barre. All told, ...

  9. De Moivre's formula - Wikipedia

    en.wikipedia.org/wiki/De_Moivre's_formula

    Since cosh x + sinh x = e x, an analog to de Moivre's formula also applies to the hyperbolic trigonometry. For all integers n, (⁡ + ⁡) = ⁡ + ⁡. If n is a rational number (but not necessarily an integer), then cosh nx + sinh nx will be one of the values of (cosh x + sinh x) n. [4]

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