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Use unlabeled aligned equations
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lib/node_modules/@stdlib/math/base/special/atan2/lib/atan2.js

+2-2
Original file line numberDiff line numberDiff line change
@@ -72,7 +72,7 @@ var PI = require( '@stdlib/constants/math/float64-pi' );
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* ## Special Cases
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*
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* ```tex
75-
* \begin{align}
75+
* \begin{align*}
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* \operatorname{atan2}(y,\mathrm{NaN}) &= \mathrm{NaN}\\
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* \operatorname{atan2}(\mathrm{NaN},x) &= \mathrm{NaN}\\
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* \operatorname{atan2}( +0,x \ge 0 ) &= +0 \\
@@ -88,7 +88,7 @@ var PI = require( '@stdlib/constants/math/float64-pi' );
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* \operatorname{atan2}(y<0, -\infty) &= -\Pi \\
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* \operatorname{atan2}(+\infty, x ) &= +\tfrac{\Pi}{2} \\
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* \operatorname{atan2}(-\infty, x ) &= -\tfrac{\Pi}{2} \\
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* \end{align}
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* \end{align*}
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* ```
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*
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* @param {number} y - numerator

lib/node_modules/@stdlib/math/base/special/fresnel/lib/fresnel.js

+4-4
Original file line numberDiff line numberDiff line change
@@ -60,19 +60,19 @@ var sc = [ 0.0, 0.0 ]; // WARNING: not thread safe
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* Evaluates the Fresnel integrals
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*
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* ```tex
63-
* \begin{align}
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* \begin{align*}
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* \operatorname{S}(x) &= \int_0^x \sin\left(\frac{\pi}{2} t^2\right)\,\mathrm{d}t, \\
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* \operatorname{C}(x) &= \int_0^x \cos\left(\frac{\pi}{2} t^2\right)\,\mathrm{d}t.
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* \end{align}
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* \end{align*}
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* ```
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*
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* The integrals are evaluated by a power series for \\( x < 1 \\). For \\( x >= 1 \\) auxiliary functions \\( f(x) \\) and \\( g(x) \\) are employed such that
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*
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* ```tex
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* \begin{align}
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* \begin{align*}
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* \operatorname{C}(x) &= \frac{1}{2} + f(x) \sin\left( \frac{\pi}{2} x^2 \right) - g(x) \cos\left( \frac{\pi}{2} x^2 \right), \\
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* \operatorname{S}(x) &= \frac{1}{2} - f(x) \cos\left( \frac{\pi}{2} x^2 \right) - g(x) \sin\left( \frac{\pi}{2} x^2 \right).
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* \end{align}
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* \end{align*}
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* ```
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*
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* ## Notes

lib/node_modules/@stdlib/math/base/special/gamma-delta-ratio/lib/gamma_delta_ratio_lanczos.js

+2-2
Original file line numberDiff line numberDiff line change
@@ -63,10 +63,10 @@ var FACTORIAL_169 = 4.269068009004705e+304;
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* - When \\( z < \epsilon \\), we get spurious numeric overflow unless we're very careful. This can occur either inside `lanczosSum(z)` or in the final combination of terms. To avoid this, split the product up into 2 (or 3) parts:
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*
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* ```tex
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* \begin{align}
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* \begin{align*}
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* G(z) / G(L) &= 1 / (z \cdot G(L)) ; z < \eps, L = z + \delta = \delta \\
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* z * G(L) &= z * G(lim) \cdot (G(L)/G(lim)) ; lim = \text{largest factorial}
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* \end{align}
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* \end{align*}
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* ```
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*
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* @private

lib/node_modules/@stdlib/math/base/special/gammaln/lib/gammaln.js

+6-6
Original file line numberDiff line numberDiff line change
@@ -91,11 +91,11 @@ var TT = -3.63867699703950536541e-18; // 0xBC50C7CAA48A971F => TT = -(tail of TF
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* For example,
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*
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* ```tex
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* \begin{align}
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* \begin{align*}
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* \operatorname{lgamma}(7.3) &= \ln(6.3) + \operatorname{lgamma}(6.3) \\
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* &= \ln(6.3 \cdot 5.3) + \operatorname{lgamma}(5.3) \\
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* &= \ln(6.3 \cdot 5.3 \cdot 4.3 \cdot 3.3 \cdot2.3) + \operatorname{lgamma}(2.3)
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* \end{align}
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* \end{align*}
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* ```
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*
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* 2. Compute a polynomial approximation of \\(\mathrm{lgamma}\\) around its minimum (\\(\mathrm{ymin} = 1.461632144968362245\\)) to maintain monotonicity. On the interval \\(\[\mathrm{ymin} - 0.23, \mathrm{ymin} + 0.27]\\) (i.e., \\(\[1.23164,1.73163]\\)), we let \\(z = x - \mathrm{ymin}\\) and use
@@ -183,10 +183,10 @@ var TT = -3.63867699703950536541e-18; // 0xBC50C7CAA48A971F => TT = -(tail of TF
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* and
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*
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* ```tex
186-
* \begin{align}
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* \begin{align*}
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* \operatorname{lgamma}(x) &= \ln(|\Gamma(x)|) \\
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* &= \ln\biggl(\frac{\pi}{|x \sin(\pi x)|}\biggr) - \operatorname{lgamma}(-x)
189-
* \end{align}
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* \end{align*}
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* ```
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*
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* <!-- <note> -->
@@ -199,15 +199,15 @@ var TT = -3.63867699703950536541e-18; // 0xBC50C7CAA48A971F => TT = -(tail of TF
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* ## Special Cases
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*
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* ```tex
202-
* \begin{align}
202+
* \begin{align*}
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* \operatorname{lgamma}(2+s) &\approx s (1-\gamma) & \mathrm{for\ tiny\ s} \\
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* \operatorname{lgamma}(x) &\approx -\ln(x) & \mathrm{for\ tiny\ x} \\
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* \operatorname{lgamma}(1) &= 0 & \\
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* \operatorname{lgamma}(2) &= 0 & \\
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* \operatorname{lgamma}(0) &= \infty & \\
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* \operatorname{lgamma}(\infty) &= \infty & \\
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* \operatorname{lgamma}(-\mathrm{integer}) &= \pm \infty
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* \end{align}
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* \end{align*}
211211
* ```
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*
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*

lib/node_modules/@stdlib/math/base/special/polygamma/lib/polycotpi.js

+2-2
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@@ -162,10 +162,10 @@ function calculateDerivatives( n ) {
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* with constant \\( C\[0,1\] = -1 \\) and all other \\( C\[k,n\] = 0 \)). Then for each \\( k < n+1 \\):
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*
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* ```tex
165-
* \begin{align}
165+
* \begin{align*}
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* C[k-1, n+1] &-= k * C[k, n]; \\
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* C[k+1, n+1] &+= (k-n-1) * C[k, n];
168-
* \end{align}
168+
* \end{align*}
169169
* ```
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*
171171
* - Note that there are many different ways of representing this derivative thanks to the many trigonometric identities available. In particular, the sum of powers of cosines could be replaced by a sum of cosine multiple angles, and, indeed, if you plug the derivative into Mathematica, this is the form it will give. The two forms are related via the Chebeshev polynomials of the first kind and \\( T_n(\cos(x)) = \cos(n x) \\). The polynomial form has the great advantage that all the cosine terms are zero at half integer arguments - right where this function has it's minimum - thus avoiding cancellation error in this region.

lib/node_modules/@stdlib/math/base/special/sinc/lib/sinc.js

+2-2
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@@ -43,12 +43,12 @@ var PI = require( '@stdlib/constants/math/float64-pi' );
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* ## Special Cases
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*
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* ```tex
46-
* \begin{align}
46+
* \begin{align*}
4747
* \operatorname{sinc}(0) &= 1 & \\
4848
* \operatorname{sinc}(\infty) &= 0 & \\
4949
* \operatorname{sinc}(-\infty) &= 0 & \\
5050
* \operatorname{sinc}(\mathrm{NaN}) &= \mathrm{NaN}
51-
* \end{align}
51+
* \end{align*}
5252
* ```
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*
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*

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