docs: add equations

lib/node_modules/@stdlib/math/base/special/exp10/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Base `10` [exponential function][exponential-function].
 
+<section class="intro">
+
+The [base-10 exponential function][exponential-function] is defined as
+
+<!-- <equation class="equation" label="eq:base10_exponential_function" align="center" raw="y = 10^x" alt="Base-10 exponential function"> -->
+
+```math
+y = 10^x
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/exp2/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Base `2` [exponential function][exponential-function].
 
+<section class="intro">
+
+The [base-2 exponential function][exponential-function] is defined as
+
+<!-- <equation class="equation" label="eq:base2_exponential_function" align="center" raw="y = 2^x" alt="Base-2 exponential function"> -->
+
+```math
+y = 2^x
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/expm1/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `exp(x) - 1`.
 
+<section class="intro">
+
+The function computes `exp(x) - 1` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:expm1_function" align="center" raw="y = e^x - 1" alt="Exponential function minus one"> -->
+
+```math
+y = e^x - 1
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/ln/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Evaluate the [natural logarithm][natural-logarithm] of a double-precision floating-point number.
 
+<section class="intro">
+
+The [natural logarithm][natural-logarithm] is defined as
+
+<!-- <equation class="equation" label="eq:natural_logarithm" align="center" raw="y = \ln(x) = \log_e(x)" alt="Natural logarithm definition"> -->
+
+```math
+y = \ln(x) = \log_e(x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/lnf/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Evaluate the [natural logarithm][natural-logarithm] of a single-precision floating-point number.
 
+<section class="intro">
+
+The [natural logarithm][natural-logarithm] is defined as
+
+<!-- <equation class="equation" label="eq:natural_logarithm" align="center" raw="y = \ln(x) = \log_e(x)" alt="Natural logarithm definition"> -->
+
+```math
+y = \ln(x) = \log_e(x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/log/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the base `b` [logarithm][logarithm] of a double-precision floating-point number.
 
+<section class="intro">
+
+The [logarithm][logarithm] with an arbitrary base is defined as
+
+<!-- <equation class="equation" label="eq:logarithm" align="center" raw="y = \log_b(x) \quad \text{such that} \quad b^y = x" alt="Logarithm with arbitrary base"> -->
+
+```math
+y = \log_b(x) \quad \text{such that} \quad b^y = x
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/log1mexp/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Evaluates the [natural logarithm][@stdlib/math/base/special/ln] of `1-exp(-|x|)`.
 
+<section class="intro">
+
+The function computes the natural logarithm of `1-exp(-|x|)` accurately
+
+<!-- <equation class="equation" label="eq:log1mexp_function" align="center" raw="y = \ln(1 - e^{-|x|})" alt="Natural logarithm of one minus exponential"> -->
+
+```math
+y = \ln(1 - e^{-|x|})
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/log1p/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Evaluate the [natural logarithm][@stdlib/math/base/special/ln] of `1+x`.
 
+<section class="intro">
+
+The function computes the [natural logarithm][natural-logarithm] of `1+x` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:log1p_function" align="center" raw="y = \ln(1 + x)" alt="Natural logarithm of one plus x"> -->
+
+```math
+y = \ln(1 + x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -197,6 +213,8 @@ int main( void ) {
 
 <section class="links">
 
+[natural-logarithm]: https://en.wikipedia.org/wiki/Natural_logarithm
+
 <!-- <related-links> -->
 
 [@stdlib/math/base/special/ln]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ln

lib/node_modules/@stdlib/math/base/special/log1pexp/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Evaluates the [natural logarithm][@stdlib/math/base/special/ln] of `1+exp(x)`.
 
+<section class="intro">
+
+The function computes the natural logarithm of `1+exp(x)`, also known as the softplus function
+
+<!-- <equation class="equation" label="eq:log1pexp_function" align="center" raw="y = \ln(1 + e^x)" alt="Natural logarithm of one plus exponential"> -->
+
+```math
+y = \ln(1 + e^x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/log1pf/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Evaluate the [natural logarithm][@stdlib/math/base/special/lnf] of `1+x` as a single‐precision floating-point number.
 
+<section class="intro">
+
+The function computes the [natural logarithm][natural-logarithm] of `1+x` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:log1p_function" align="center" raw="y = \ln(1 + x)" alt="Natural logarithm of one plus x"> -->
+
+```math
+y = \ln(1 + x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -190,6 +206,8 @@ int main( void ) {
 
 <section class="links">
 
+[natural-logarithm]: https://en.wikipedia.org/wiki/Natural_logarithm
+
 [@stdlib/math/base/special/lnf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/lnf
 
 <!-- <related-links> -->

lib/node_modules/@stdlib/math/base/special/log1pmx/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Evaluate `ln(1+x) - x`.
 
+<section class="intro">
+
+The function computes `ln(1+x) - x` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:log1pmx_function" align="center" raw="y = \ln(1 + x) - x" alt="Natural logarithm of one plus x minus x"> -->
+
+```math
+y = \ln(1 + x) - x
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/logf/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the base `b` [logarithm][logarithm] of a single-precision floating-point number.
 
+<section class="intro">
+
+The [logarithm][logarithm] with an arbitrary base is defined as
+
+<!-- <equation class="equation" label="eq:logarithm" align="center" raw="y = \log_b(x) \quad \text{such that} \quad b^y = x" alt="Logarithm with arbitrary base"> -->
+
+```math
+y = \log_b(x) \quad \text{such that} \quad b^y = x
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/xlog1py/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `x * ln(y+1)` so that the result is `0` if `x = 0`.
 
+<section class="intro">
+
+The function computes `x * ln(1+y)`, returning `0` when `x = 0`
+
+<!-- <equation class="equation" label="eq:xlog1py_function" align="center" raw="f(x, y) = \begin{cases} x \cdot \ln(1 + y) & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}" alt="x times the natural logarithm of one plus y"> -->
+
+```math
+f(x, y) = \begin{cases} x \cdot \ln(1 + y) & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/xlogy/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `x * ln(y)` so that the result is `0` if `x = 0`.
 
+<section class="intro">
+
+The function computes `x * ln(y)`, returning `0` when `x = 0`
+
+<!-- <equation class="equation" label="eq:xlogy_function" align="center" raw="f(x, y) = \begin{cases} x \cdot \ln(y) & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}" alt="x times the natural logarithm of y"> -->
+
+```math
+f(x, y) = \begin{cases} x \cdot \ln(y) & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/xlogyf/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `x * ln(y)` so that the result is `0` if `x = 0` for single-precision floating-point numbers `x` and `y`.
 
+<section class="intro">
+
+The function computes `x * ln(y)`, returning `0` when `x = 0`
+
+<!-- <equation class="equation" label="eq:xlogy_function" align="center" raw="f(x, y) = \begin{cases} x \cdot \ln(y) & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}" alt="x times the natural logarithm of y"> -->
+
+```math
+f(x, y) = \begin{cases} x \cdot \ln(y) & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage