From 01f91daefbc7036fddabcfa9090027d790df7926 Mon Sep 17 00:00:00 2001
From: Karan Anand <anandkarancompsci@gmail.com>
Date: Thu, 27 Aug 2026 10:01:36 +0530
Subject: [PATCH] docs: add equations to hyperbolic function READMEs

Add defining equations with exponential definitions to the intro
sections of sinh, cosh, tanh, coth, sech, csch and their
single-precision variants.

Ref: https://github.com/stdlib-js/metr-issue-tracker/issues/1257
---
 .../@stdlib/math/base/special/cosh/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/coshf/README.md    | 16 ++++++++++++++++
 .../@stdlib/math/base/special/coth/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/csch/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/sech/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/sinh/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/sinhf/README.md    | 16 ++++++++++++++++
 .../@stdlib/math/base/special/tanh/README.md     | 16 ++++++++++++++++
 8 files changed, 128 insertions(+)

diff --git a/lib/node_modules/@stdlib/math/base/special/cosh/README.md b/lib/node_modules/@stdlib/math/base/special/cosh/README.md
index 26eb5d368587..feecd33c22eb 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosh/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosh/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic cosine][hyperbolic-cosine] of a double-precision floating-point number.
 
+<section class="intro">
+
+The [hyperbolic cosine][hyperbolic-cosine] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_cosine" align="center" raw="y = \cosh(x) = \frac{e^x + e^{-x}}{2}" alt="Hyperbolic cosine function"> -->
+
+```math
+y = \cosh(x) = \frac{e^x + e^{-x}}{2}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/coshf/README.md b/lib/node_modules/@stdlib/math/base/special/coshf/README.md
index 4baccf71b573..795d8d1495ed 100644
--- a/lib/node_modules/@stdlib/math/base/special/coshf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/coshf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic cosine][hyperbolic-cosine] of a single-precision floating-point number.
 
+<section class="intro">
+
+The [hyperbolic cosine][hyperbolic-cosine] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_cosine" align="center" raw="y = \cosh(x) = \frac{e^x + e^{-x}}{2}" alt="Hyperbolic cosine function"> -->
+
+```math
+y = \cosh(x) = \frac{e^x + e^{-x}}{2}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/coth/README.md b/lib/node_modules/@stdlib/math/base/special/coth/README.md
index 188a9adc0cd0..c1d9cd4f2b48 100644
--- a/lib/node_modules/@stdlib/math/base/special/coth/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/coth/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic cotangent][hyperbolic-functions] of a number.
 
+<section class="intro">
+
+The [hyperbolic cotangent][hyperbolic-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_cotangent" align="center" raw="y = \coth(x) = \frac{e^x + e^{-x}}{e^x - e^{-x}}" alt="Hyperbolic cotangent function"> -->
+
+```math
+y = \coth(x) = \frac{e^x + e^{-x}}{e^x - e^{-x}}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/csch/README.md b/lib/node_modules/@stdlib/math/base/special/csch/README.md
index 92df82e8eb7f..ab22859b6388 100644
--- a/lib/node_modules/@stdlib/math/base/special/csch/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/csch/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic cosecant][hyperbolic-functions] of a number.
 
+<section class="intro">
+
+The [hyperbolic cosecant][hyperbolic-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_cosecant" align="center" raw="y = \operatorname{csch}(x) = \frac{2}{e^x - e^{-x}}" alt="Hyperbolic cosecant function"> -->
+
+```math
+y = \mathop{\mathrm{csch}}(x) = \frac{2}{e^x - e^{-x}}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/sech/README.md b/lib/node_modules/@stdlib/math/base/special/sech/README.md
index f4f11caa0c61..0e9f5e0cdfc2 100644
--- a/lib/node_modules/@stdlib/math/base/special/sech/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sech/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic secant][hyperbolic-functions] of a double-precision floating-point number.
 
+<section class="intro">
+
+The [hyperbolic secant][hyperbolic-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_secant" align="center" raw="y = \operatorname{sech}(x) = \frac{2}{e^x + e^{-x}}" alt="Hyperbolic secant function"> -->
+
+```math
+y = \mathop{\mathrm{sech}}(x) = \frac{2}{e^x + e^{-x}}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/sinh/README.md b/lib/node_modules/@stdlib/math/base/special/sinh/README.md
index e1cec5e31df1..306eaac22e10 100644
--- a/lib/node_modules/@stdlib/math/base/special/sinh/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sinh/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic sine][hyperbolic-sine] of a double-precision floating-point number.
 
+<section class="intro">
+
+The [hyperbolic sine][hyperbolic-sine] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_sine" align="center" raw="y = \sinh(x) = \frac{e^x - e^{-x}}{2}" alt="Hyperbolic sine function"> -->
+
+```math
+y = \sinh(x) = \frac{e^x - e^{-x}}{2}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/sinhf/README.md b/lib/node_modules/@stdlib/math/base/special/sinhf/README.md
index 684079d352c3..a9f69c22f3dc 100644
--- a/lib/node_modules/@stdlib/math/base/special/sinhf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sinhf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic sine][hyperbolic-sine] of a single-precision floating-point number.
 
+<section class="intro">
+
+The [hyperbolic sine][hyperbolic-sine] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_sine" align="center" raw="y = \sinh(x) = \frac{e^x - e^{-x}}{2}" alt="Hyperbolic sine function"> -->
+
+```math
+y = \sinh(x) = \frac{e^x - e^{-x}}{2}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/tanh/README.md b/lib/node_modules/@stdlib/math/base/special/tanh/README.md
index 26492ea92bf8..ffdd4c525447 100644
--- a/lib/node_modules/@stdlib/math/base/special/tanh/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/tanh/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [hyperbolic tangent][hyperbolic-tangent] of a double-precision floating-point number.
 
+<section class="intro">
+
+The [hyperbolic tangent][hyperbolic-tangent] function is defined as
+
+<!-- <equation class="equation" label="eq:hyperbolic_tangent" align="center" raw="y = \tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}" alt="Hyperbolic tangent function"> -->
+
+```math
+y = \tanh(x) = \frac{e^x - e^{-x}}{e^x + e^{-x}}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage