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- 23:16, 21 October 2017 (diff | hist) . . (+403) . . N Doubling identity for cosh (3) (Created page with "==Theorem== The following formula holds: $$\cosh(2z)=\cosh^2(z)+\sinh^2(z),$$ where $\cosh$ denotes hyperbolic cosine and $\sinh$ denotes hyperbolic sine. =...") (current)
- 23:15, 21 October 2017 (diff | hist) . . (0) . . Doubling identity for cosh (2) (current)
- 23:14, 21 October 2017 (diff | hist) . . (+419) . . N Doubling identity for cosh (2) (Created page with "==Theorem== The following formula holds: $$\cosh(2z)=2\sinh^2(z)+1,$$ where $\cosh$ denotes hyperbolic cosine and $\sinh$ denotes hyperbolic sine. ==Proof==...")
- 22:54, 21 October 2017 (diff | hist) . . (+374) . . N Doubling identity for cosh (1) (Created page with "==Theorem== The following formula holds: $$\cosh(2z)=2\cosh^2(z)-1,$$ where $\cosh$ denotes hyperbolic cosine. ==Proof== ==References== * {{BookReference|Handbook o...") (current)
- 22:53, 21 October 2017 (diff | hist) . . (+438) . . N Doubling identity for sinh (2) (Created page with "==Theorem== The following formula holds: $$\sinh(2z)=\dfrac{2\tanh(z)}{1-\tanh^2(z)},$$ where $\sinh$ denotes hyperbolic sine and $\tanh$ denotes tanh|hyperbolic ta...") (current)
- 22:52, 21 October 2017 (diff | hist) . . (+425) . . N Doubling identity for sinh (1) (Created page with "==Theorem== The following formula holds: $$\sinh(2z)=2\sinh(z)\cosh(z),$$ where $\sinh$ denotes hyperbolic sine and $\cosh$ denotes hyperbolic cosine. ==Pro...") (current)
- 22:51, 21 October 2017 (diff | hist) . . (+4) . . Halving identity for tangent (3) (current)
- 22:50, 21 October 2017 (diff | hist) . . (+504) . . N Halving identity for tangent (3) (Created page with "==Theorem== The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \dfrac{\sinh(z)}{\cosh(z)+1},$$ where $\tanh$ denotes hyperbolic tangent, $\sinh$ denot...")
- 22:49, 21 October 2017 (diff | hist) . . (+510) . . N Halving identity for tangent (2) (Created page with "==Theorem== The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \dfrac{\cosh(z)-1}{\sinh(z)},$$ where $\tanh$ denotes hyperbolic tangent, $\cosh$ denot...") (current)
- 22:48, 21 October 2017 (diff | hist) . . (+26) . . Halving identity for tangent (1) (current)
- 22:47, 21 October 2017 (diff | hist) . . (-189) . . Halving identity for tangent (1)
- 22:47, 21 October 2017 (diff | hist) . . (+625) . . N Halving identity for tangent (1) (Created page with "==Theorem== The following formula holds: $$\tanh \left( \dfrac{z}{2} \right) = \sqrt{ \dfrac{\cosh(z)-1}{2} },$$ where $\tanh$ denotes hyperbolic tangent and $\cosh$...")
- 22:46, 21 October 2017 (diff | hist) . . (+4) . . Halving identity for cosh (current)
- 22:45, 21 October 2017 (diff | hist) . . (+410) . . N Halving identity for cosh (Created page with "==Theorem== The following formula holds: $$\cosh \left( \dfrac{z}{2} \right) = \sqrt{ \dfrac{\cosh(z)+1}{2} },$$ where $\cosh$ denotes hyperbolic cosine. ==Proof==...")
- 22:43, 21 October 2017 (diff | hist) . . (+441) . . N Halving identity for sinh (Created page with "==Theorem== The following formula holds: $$\sinh \left( \dfrac{z}{2} \right) = \sqrt{ \dfrac{\cosh(z)-1}{2} },$$ where $\sinh$ denotes hyperbolic sine and $\cosh$ den...") (current)
- 22:42, 21 October 2017 (diff | hist) . . (+12) . . Coth of a sum
- 22:41, 21 October 2017 (diff | hist) . . (+388) . . N Coth of a sum (Created page with "==Theorem== The following formula holds: $$\coth(z_1+z_2)=\dfrac{\coth(z_1)\coth(z_2)+1}{\cosh(z_1)+\coth(z_2)},$$ where $\coth$ denotes hyperbolic cotangent. ==Proo...")
- 22:40, 21 October 2017 (diff | hist) . . (+7) . . Tanh of a sum (current)
- 22:40, 21 October 2017 (diff | hist) . . (+389) . . N Tanh of a sum (Created page with "==Theorem== The following formula holds: $$\mathrm{tanh}(z_1+z_2) = \dfrac{\tanh(z_1)+\tanh(z_2)}{1+\tanh(z_1)\tanh(z_2)},$$ where $\tanh$ denotes hyperbolic tangent....")
- 22:39, 21 October 2017 (diff | hist) . . (+7) . . Cosh of a sum (current)
- 22:38, 21 October 2017 (diff | hist) . . (+415) . . N Cosh of a sum (Created page with "==Theorem== The following formula holds: $$\cosh(z_1+z_2) = \cosh(z_1)\cosh(z_2) + \sinh(z_1)\sinh(z_2),$$ where $\cosh$ denotes hyperbolic cosine and $\sinh$ denotes...")
- 22:37, 21 October 2017 (diff | hist) . . (+416) . . N Sinh of a sum (Created page with "==Theorem== The following formula holds: $$\sinh(z_1+z_2)=\sinh(z_1)\cosh(z_2)+\cosh(z_1)\sinh(z_2),$$ where $\sinh$ denotes hyperbolic sine and $\cosh$ denotes cos...") (current)
- 22:36, 21 October 2017 (diff | hist) . . (+336) . . N Tanh is odd (Created page with "==Theorem== The following formula holds: $$\tanh(-z)=-\tanh(z),$$ where $\tanh$ denotes hyperbolic tangent. ==Proof== ==References== * {{BookReference|Handbook of m...") (current)
- 22:35, 21 October 2017 (diff | hist) . . (+331) . . N Cosh is even (Created page with "==Theorem== The following formula holds: $$\cosh(-z)=\cosh(z),$$ where $\cosh$ denotes hyperbolic cosine. ==Proof== ==References== * {{BookReference|Handbook of mat...") (current)
- 22:34, 21 October 2017 (diff | hist) . . (+6) . . Sinh is odd (current)
- 22:33, 21 October 2017 (diff | hist) . . (+44) . . Difference of cosh and sinh (current)
- 22:33, 21 October 2017 (diff | hist) . . (+341) . . N Sinh is odd (Created page with "==Theorem== The following formula holds: $$\sinh(-z)=-\sinh(z),$$ where $\sinh$ denotes hyperbolic sine. ==Proof== ==References== * {{BookReference|Handbook of math...")
- 22:32, 21 October 2017 (diff | hist) . . (+5) . . Difference of cosh and sinh
- 22:32, 21 October 2017 (diff | hist) . . (+9) . . Difference of cosh and sinh (Undo revision 8735 by Tom (talk))
- 22:31, 21 October 2017 (diff | hist) . . (-9) . . Difference of cosh and sinh
- 22:31, 21 October 2017 (diff | hist) . . (+385) . . N Difference of cosh and sinh (Created page with "==Theorem== The following formula holds: $$\cosh(z) - \sinh(z) = e^{-z},$$ where $\cosh$ denotes hyperbolic cosine, $\sinh$ denotes hyperbolic sine, and $e^{...")
- 22:30, 21 October 2017 (diff | hist) . . (+21) . . Sum of cosh and sinh (current)
- 22:29, 21 October 2017 (diff | hist) . . (+44) . . Pythagorean identity for coth and csch (current)
- 22:29, 21 October 2017 (diff | hist) . . (+449) . . N Sum of cosh and sinh (Created page with "==Theorem== The following formula holds: $$\cosh(z) + \sinh(z) = e^z,$$ where $\cosh$ denotes hyperbolic cosine, $\mathrm{sinh}$ denotes hyperbolic sine, and...")
- 22:28, 21 October 2017 (diff | hist) . . (+412) . . N Pythagorean identity for coth and csch (Created page with "==Theorem== The following formula holds: $$\mathrm{coth}^2(z)-\mathrm{csch}^2(z)=1,$$ where $\mathrm{coth}$ denotes hyperbolic cotangent and $\mathrm{csch}$ denotes [...")
- 22:26, 21 October 2017 (diff | hist) . . (+32) . . Pythagorean identity for tanh and sech (current)
- 22:25, 21 October 2017 (diff | hist) . . (+446) . . N Pythagorean identity for tanh and sech (Created page with "==Theorem== The following formula holds: $$\mathrm{tanh}^2(z)+\mathrm{sech}^2(z)=1,$$ where $\mathrm{tanh}$ denotes the hyperbolic tangent and $\mathrm{sech}$ denotes...")
- 22:25, 21 October 2017 (diff | hist) . . (+176) . . Pythagorean identity for sinh and cosh (current)
- 22:24, 21 October 2017 (diff | hist) . . (+49) . . Tanh (→Properties)
- 22:23, 21 October 2017 (diff | hist) . . (+32) . . Period of tanh (current)
- 16:07, 21 October 2017 (diff | hist) . . (+7) . . Airy Bi (current)
- 04:30, 15 September 2017 (diff | hist) . . (+39) . . Main Page (→Matrix functions)
- 03:56, 15 September 2017 (diff | hist) . . (+192) . . Main Page
- 22:10, 26 August 2017 (diff | hist) . . (+73) . . Main Page (→Special functions)
- 22:09, 26 August 2017 (diff | hist) . . (+24) . . Laplace transform
- 22:08, 26 August 2017 (diff | hist) . . (+30) . . Two-dimensional Laplace transform (current)
- 22:08, 26 August 2017 (diff | hist) . . (+444) . . N Unit step function (Created page with "The unit step function $U \colon \mathbb{R} \rightarrow \left\{ 0, \dfrac{1}{2}, 1 \right\}$ is defined by $$U(t)=\left\{ \begin{array}{ll} 0 &, \quad t<0 \\ \dfrac{1}{2}&, \q...") (current)
- 22:06, 26 August 2017 (diff | hist) . . (+414) . . N Two-dimensional Laplace transform (Created page with "The two-dimensional Laplace transform of a function $f$ is $$\mathscr{L}\{f\}(z_1,z_2)=\displaystyle\int_0^{\infty} \displaystyle\int_0^{\infty} e^{-z_1x-z_2y} \mathrm{d}x \ma...")
- 22:05, 26 August 2017 (diff | hist) . . (+27) . . Laplace transform
- 22:03, 26 August 2017 (diff | hist) . . (+50) . . Laplace transform
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