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| | === dashboard === | | === dashboard === |
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| − | ==IMCOSH==
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| − | Returns the hyperbolic cosine of a complex number.
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| − | ===Syntax===
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| − | <code>IMCOSH( z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − | ===Sematics===
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| − | <code>IMCOSH("a+bj")</code> calculates
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| − | : <math> \cosh{(a)}\, \cos{(b)}+ \sinh{(a)}\, \sin{(b)} \mbox{ j} </math>
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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| − | ==IMCOT==
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| − | Returns the cotangent of a complex number
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| − | ===Syntax===
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| − | <code>IMCOT( z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − | ===Semantics===
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| − | <code>IMCOT( z )</code> is equivalent to <code>IMDIV(IMCOS(z);IMSIN(z))</code>.
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| − | To get better accuracy it is not implemented that way. With the notation <code>IMCOT("a+bj")="c+dj"</code> the used formulas are
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| − | : real part <math> c = \frac {\sin(2a)} {\cosh(2b)-\cos(2a)}</math>
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| − | : imaginary part <math>d= \frac {-\sinh(2b) } {\cosh(2b)-\cos(2a)}</math>
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| − |
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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| − | ==IMCSC==
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| − | Returns the cosecant of a complex number.
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| − | ===Syntax===
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| − | <code>IMCSC( z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − |
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| − | ===Semantics===
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| − | <code>IMCSC( z )</code> is equivalent to <code>IMDIV(1;IMSIN( z ))</code>.
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| − |
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| − | To get better accuracy it is not implemented that way. With the notation <code>IMCOT("a+bj")="c+dj"</code> the used formulas are
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| − | : real part <math> c = \frac{2\sin(a)\,\cosh(b)}{\cosh(2b)-\cos(2a)}</math>
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| − | : imaginary part <math>d = \frac{-2\cos(a)\,\sinh(b)}{\cosh(2b)-\cos(2a)}</math>
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| − |
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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| − | ==IMCSCH==
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| − | Returns the hyperbolic cosecant of a complex number.
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| − |
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| − | ===Syntax===
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| − | <code>IMCSCH( z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − |
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| − | ===Semantics===
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| − | <code>IMCSCH( z )</code> is equivalent to <code>IMDIV(1;IMSINH( z ))</code>.
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| − |
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| − | To get better accuracy it is not implemented that way. With the notation <code>IMCOT("a+bj")="c+dj"</code> the used formulas are
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| − | : real part <math> c = \frac{2\sinh(2a)\,\cos(b)}{\cosh(2a)-\cos(2b)}</math>
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| − | : imaginary part <math>d = \frac{-2\cosh(2a)\,\sin(b)}{\cosh(2a)-\cos(2b)}</math>
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| − |
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| − |
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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| − |
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| − |
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| − | ==IMSINH==
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| − | Returns the hyperbolic sine of a complex number.
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| − |
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| − | ===Syntax===
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| − | <code>IMSINH( z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − |
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| − | ===Semantics===
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| − | <code>IMSINH("a+bj")</code> calculates
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| − | : <math>\sinh{(a)}\, \cos{(b)}+ \cosh{(a)}\, \sin{(b)} \mbox{ j}</math>
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| − |
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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| − | ==IMSEC==
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| − | Returns the secant of a complex number.
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| − | ===Syntax===
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| − | <code>IMSEC( z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − |
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| − | ===Semantics===
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| − | <code>IMSEC( z )</code> is equivalent to <code>IMDIV(1;IMCOS( z ))</code>.
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| − |
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| − | To get better accuracy it is not implemented that way. With the notation <code>IMCOT("a+bj")="c+dj"</code> the used formulas are
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| − | : real part <math> c = \frac{2\cos(a)\,\cosh(b)}{\cosh(2b)+\cos(2a)}</math>
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| − | : imaginary part <math>d = \frac{2\sin(a)\,\sinh(b)}{\cosh(2b)+\cos(2a)}</math>
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| − |
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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| − |
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| − |
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| − | ==IMSECH==
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| − | Returns the hyperbolic secant of a complex number.
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| − |
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| − | ===Syntax===
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| − | <code>IMSECH( z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − |
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| − | ===Semantics===
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| − | <code>IMSECH( z )</code> is equivalent to <code>IMDIV(1;IMCOSH( z ))</code>.
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| − |
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| − | To get better accuracy it is not implemented that way. With the notation <code>IMCOT("a+bj")="c+dj"</code> the used formulas are
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| − | : real part <math>c = \frac{2\cosh(2a)\,\cos(b)}{\cosh(2a)+\cos(2b)}</math>
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| − | : imaginary part <math>d = \frac{-2\sinh(2a)\,\sin(b)}{\cosh(2a)+\cos(2b)}</math>
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| − |
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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| − |
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| − |
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| − | ==IMTAN==
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| − | Returns the tangent of a complex number.
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| − | ===Syntax===
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| − | <code>IMTAN( Z )</code>
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| − | : where z is a complex number as described in [[Documentation/How_Tos/Calc:_Complex_Number_functions]]
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| − |
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| − | ===Semantics===
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| − | <code>IMTAN( Z )</code> is equivalent to <code>IMDIV(IMSIN( z );IMCOS( z ))</code>.
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| − |
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| − | To get better accuracy it is not implemented that way. With the notation <code>IMCOT("a+bj")="c+dj"</code> the used formulas are
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| − | : real part <math>c = \frac{\sin(2a)}{\cos(2a)+\cosh(2b)}</math>
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| − | : imaginary part <math>d = \frac{\sinh(2b)}{\cos(2a)+\cosh(2b)}</math>
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| − |
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| − |
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| − | ===Issues===
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| − | The function is not implemented in versions before AOO 4.0 and before LibO 3.7.
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<math>\scriptstyle \sqrt {n-1}</math>
<math>\sqrt {n-1}</math>
<math> s_{X_1 - X_2}</math>
<math>1-P( -|z| \le Z \le |z|)</math>
<math>\textstyle \sum_{k=1}^N k^2</math>
<math>\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</math>
<math>\frac{1}{N} \sum_{k=2}^N k^2</math>
\frac{1} {n} \sum_{i} {(x_i - \bar x)(y_i - \bar y)}</math>
