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Relationship between hyperbolic functions and complex analysis

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#complex-analysis #complex-numbers #hyperbolic-functions
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What is the relation to $\sinh{x},\cosh{x}$ and $\sin{x},\cos{x}$

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#trigonometry #hyperbolic-functions
435
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Integral of $\arccos(x + 1)$

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#integration #indefinite-integrals #hyperbolic-functions
141
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Proving $\frac{\sinh\tau+\sinh i\sigma}{\cosh\tau+\cosh i\sigma }=-\coth\left(i\frac{\sigma+i\tau }{2}\right)$ for bipolar coordinates $(\sigma,\tau)$

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#complex-numbers #hyperbolic-functions
362
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Principal part of Laurent Series for $\frac{1}{(1-\cosh(z))^2}$

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#complex-analysis #laurent-series #hyperbolic-functions
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Prove formula $\operatorname{arctanh} x = \frac12\,\ln \left(\frac{1+x}{1-x}\right)$

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#proof-verification #hyperbolic-functions
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Fourier transform of $x / \tanh(x)$

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#fourier-transform #hyperbolic-functions
679
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Inverse Function Theorem: Proving Global Invertibility.

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#calculus #multivariable-calculus #hyperbolic-functions #inverse-function-theorem
237
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Getting function from four points

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#exponential-function #graphing-functions #binary #hyperbolic-functions
6.2k
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Proof for hyperbolic trigonometric identities

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#trigonometry #hyperbolic-functions
223
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Find min distance from y = cosh x to y = x

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#hyperbolic-functions
132
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Solve second order differential equation with cosh using frobenios method

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#ordinary-differential-equations #power-series #hyperbolic-functions #frobenius-method
915
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Is the similarity between tanh and normal distribution just coincidence?

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#taylor-expansion #normal-distribution #hyperbolic-functions
156
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Why is the domain of the hyperbolic function $\sinh x$ is symmetric about the origin?

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#hyperbolic-functions
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Basis formed by hyperbolic functions

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#linear-algebra #vector-spaces #hyperbolic-functions #change-of-basis

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