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Nov 10, 2025
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some katex improvements #153

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95c6e12
some katex improvements
jorenham Nov 9, 2025
dc11450
spacing
jorenham Nov 10, 2025
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47 changes: 23 additions & 24 deletions katex.html
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Expand Up @@ -27,46 +27,45 @@
document.addEventListener("DOMContentLoaded", () => {
renderMathInElement(document.body, {
strict: "error",
throwOnError: true,
trust: true,
throwOnError: false,
delimiters: [{left: "$$", right: "$$", display: true}, {left: "$", right: "$", display: false}],
macros: {
// Beta function
"\\B": "\\mathop{\\Beta}",
// absolute value
"\\abs": String.raw`\left| #1 \right|`,

// Beta functions
"\\B": String.raw`\operatorname{\Beta}`,
"\\I": String.raw`\operatorname{I}`,

// error function
"\\erf": "\\mathop{\\mathrm{erf}}",
"\\erfc": "\\mathop{\\mathrm{erfc}}",
"\\erfi": "\\mathop{\\mathrm{erfi}}",
"\\erf": String.raw`\operatorname{\mathrm{erf}}`,
"\\erfc": String.raw`\operatorname{\mathrm{erfc}}`,
"\\erfi": String.raw`\operatorname{\mathrm{erfi}}`,

// sign function
"\\sgn": "\\mathop{\\mathrm{sgn}}",
"\\sgn": "\\operatorname{\\mathrm{sgn}}",

// kelvin functions
"\\ber": "\\mathop{\\mathrm{ber}}",
"\\berp": "\\mathop{\\mathrm{ber}'}",
"\\bei": "\\mathop{\\mathrm{bei}}",
"\\beip": "\\mathop{\\mathrm{bei}'}",
"\\ker": "\\mathop{\\mathrm{ker}}",
"\\kerp": "\\mathop{\\mathrm{ker}'}",
"\\kei": "\\mathop{\\mathrm{kei}}",
"\\keip": "\\mathop{\\mathrm{kei}'}",
"\\ber": String.raw`\operatorname{\mathrm{ber}}`,
"\\bei": String.raw`\operatorname{\mathrm{bei}}`,
"\\ker": String.raw`\operatorname{\mathrm{ker}}`,
"\\kei": String.raw`\operatorname{\mathrm{kei}}`,

// sine and cosine integrals
"\\Si": "\\mathop{\\mathrm{Si}}",
"\\Ci": "\\mathop{\\mathrm{Ci}}",
"\\Shi": "\\mathop{\\mathrm{Shi}}",
"\\Chi": "\\mathop{\\mathrm{Chi}}",
"\\Si": String.raw`\operatorname{\mathrm{Si}}`,
"\\Ci": String.raw`\operatorname{\mathrm{Ci}}`,
"\\Shi": String.raw`\operatorname{\mathrm{Shi}}`,
"\\Chi": String.raw`\operatorname{\mathrm{Chi}}`,

// falling and rising factorials
"\\fpow": "#1^{\\underline{#2}}",
"\\rpow": "#1^{\\overline{#2}}",
"\\fpow": String.raw`\left(#1\right)^{\smash{-}}_{#2}`,
"\\rpow": String.raw`\left(#1\right)^{\smash{+}}_{#2}`,

// hypergeometric functions
"\\hyp": "{}_#1F_#2\\left[{#3 \\atop #4} \\ #5 \\right]",
"\\hyp": String.raw`{}_#1F_#2\left[{#3 \atop #4} \middle| #5 \right]`,

// some missing "physics" tex package commands
"\\dd": "\\,\\mathrm{d}",
"\\dd": String.raw`\,\mathrm{d}`,
},
})
})
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82 changes: 41 additions & 41 deletions src/lib.rs
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Expand Up @@ -239,25 +239,25 @@
//!
//! # Gamma and related functions
//!
//! | Function | Description |
//! | ---------------- | ------------------------------------------------------------------- |
//! | [`gamma`] | Gamma function, $\Gamma(z)$ |
//! | [`gammaln`] | Log-gamma function, $\ln \| \Gamma(z) \|$ |
//! | [`loggamma`] | Principal branch of $\ln \Gamma(z)$ |
//! | [`gammasgn`] | Sign of [`gamma`], $\sgn(\Gamma(z))$ |
//! | [`gammainc`] | Regularized lower incomplete gamma function $P(a,x) = 1 - Q(a,x)$ |
//! | [`gammaincinv`] | Inverse of [`gammainc`], $P^{-1}(a,y)$ |
//! | [`gammaincc`] | Regularized upper incomplete gamma function $Q(a,x) = 1 - P(a,x) $ |
//! | [`gammainccinv`] | Inverse of [`gammaincc`], $Q^{-1}(a,y)$ |
//! | [`beta`] | Beta function, $\B(a,b) = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$ |
//! | [`betaln`] | Log-Beta function, $\ln \| \B(a,b) \|$ |
//! | [`betainc`] | Regularized incomplete beta function, $I_x(a,b)$ |
//! | [`betaincinv`] | Inverse of [`betainc`], $I_y^{-1}(a,b)$ |
//! | [`digamma`] | The digamma function, $\psi(z)$ |
//! | [`polygamma`] | The polygamma function, $\psi^{(n)}(x)$ |
//! | [`rgamma`] | Reciprocal of the gamma function, $\frac{1}{\Gamma(z)}$ |
//! | [`pow_rising`] | Rising factorial $\rpow{x}{m} = \frac{\Gamma(x+m)}{\Gamma(x)}$ |
//! | [`pow_falling`] | Falling factorial $\fpow{x}{m} = \frac{\Gamma(x+1)}{\Gamma(x+1-m)}$ |
//! | Function | Description |
//! | ---------------- | ----------------------------------------------------------------- |
//! | [`gamma`] | Gamma function, $\Gamma(z)$ |
//! | [`gammaln`] | Log-gamma function, $\ln\abs{\Gamma(z)}$ |
//! | [`loggamma`] | Principal branch of $\ln \Gamma(z)$ |
//! | [`gammasgn`] | Sign of [`gamma`], $\sgn(\Gamma(z))$ |
//! | [`gammainc`] | Regularized lower incomplete gamma function $P(a,x) = 1 - Q(a,x)$ |
//! | [`gammaincinv`] | Inverse of [`gammainc`], $P^{-1}(a,y)$ |
//! | [`gammaincc`] | Regularized upper incomplete gamma function $Q(a,x) = 1 - P(a,x)$ |
//! | [`gammainccinv`] | Inverse of [`gammaincc`], $Q^{-1}(a,y)$ |
//! | [`beta`] | Beta function, $\B(a,b) = {\Gamma(a)\Gamma(b) \over \Gamma(a+b)}$ |
//! | [`betaln`] | Log-Beta function, $\ln\abs{\B(a,b)}$ |
//! | [`betainc`] | Regularized incomplete beta function, $\I_x(a,b)$ |
//! | [`betaincinv`] | Inverse of [`betainc`], $\I_y^{-1}(a,b)$ |
//! | [`digamma`] | The digamma function, $\psi(z)$ |
//! | [`polygamma`] | The polygamma function, $\psi^{(n)}(x)$ |
//! | [`rgamma`] | Reciprocal of the gamma function, $\frac{1}{\Gamma(z)}$ |
//! | [`pow_rising`] | Rising factorial $\rpow x m = {\Gamma(x+m) \over \Gamma(x)}$ |
//! | [`pow_falling`] | Falling factorial $\fpow x m = {\Gamma(x+1) \over \Gamma(x+1-m)}$ |
//!
//! # Error function and Fresnel integrals
//!
Expand Down Expand Up @@ -306,14 +306,14 @@
//!
//! # Hypergeometric functions
//!
//! | Function | Description | Notation |
//! | ---------- | --------------------------------------- | ------------------------------------ |
//! | [`hyp0f0`] | Generalized hypergeometric function | $_0F_0\[\rvert\\, z\]$ |
//! | [`hyp1f0`] | Generalized hypergeometric function | $_1F_0\[a\\, \rvert\\, z\]$ |
//! | [`hyp0f1`] | Confluent hypergeometric limit function | $_0F_1\[b\\, \rvert\\, z\]$ |
//! | [`hypu`] | Confluent hypergeometric function | $U(a,b,x)$ |
//! | [`hyp1f1`] | Confluent hypergeometric function | $\hyp{1}{1}{a}{b}{\big\|\\,z}$ |
//! | [`hyp2f1`] | Gauss' hypergeometric function | $\hyp{2}{1}{a_1,a_2}{b}{\big\|\\,z}$ |
//! | Function | Description | Notation |
//! | ---------- | --------------------------------------- | -------------------------------- |
//! | [`hyp0f0`] | Generalized hypergeometric function | $_0F_0\left[ \middle\| z\right]$ |
//! | [`hyp1f0`] | Generalized hypergeometric function | $_1F_0\left[a\middle\| z\right]$ |
//! | [`hyp0f1`] | Confluent hypergeometric limit function | $_0F_1\left[b\middle\| z\right]$ |
//! | [`hypu`] | Confluent hypergeometric function | $U(a,b,x)$ |
//! | [`hyp1f1`] | Confluent hypergeometric function | $\hyp 1 1 a b z$ |
//! | [`hyp2f1`] | Gauss' hypergeometric function | $\hyp 2 1 {a_1\enspace a_2} b z$ |
//!
//! # Parabolic cylinder functions
//!
Expand Down Expand Up @@ -363,22 +363,22 @@
//! | ---------- | ---------------- | ----------------------------------- |
//! | [`kelvin`] | [`kelvin_zeros`] | Kelvin functions as complex numbers |
//! | [`ber`] | [`ber_zeros`] | Kelvin function $\ber(x)$ |
//! | [`berp`] | [`berp_zeros`] | Derivative of [`ber`], $\berp(x)$ |
//! | [`berp`] | [`berp_zeros`] | Derivative of [`ber`], $\ber\'(x)$ |
//! | [`bei`] | [`bei_zeros`] | Kelvin function $\bei(x)$ |
//! | [`beip`] | [`beip_zeros`] | Derivative of [`bei`], $\beip(x)$ |
//! | [`beip`] | [`beip_zeros`] | Derivative of [`bei`], $\bei\'(x)$ |
//! | [`ker`] | [`ker_zeros`] | Kelvin function $\ker(x)$ |
//! | [`kerp`] | [`kerp_zeros`] | Derivative of [`ker`], $\kerp(x)$ |
//! | [`kerp`] | [`kerp_zeros`] | Derivative of [`ker`], $\ker\'(x)$ |
//! | [`kei`] | [`kei_zeros`] | Kelvin function $\kei(x)$ |
//! | [`keip`] | [`keip_zeros`] | Derivative of [`kei`], $\keip(x)$ |
//! | [`keip`] | [`keip_zeros`] | Derivative of [`kei`], $\kei\'(x)$ |
//!
//! # Combinatorics
//!
//! | Function | Description |
//! | -------------- | ----------------------------------------------------------------------- |
//! | [`comb`] | $k$-combinations of $n$ things, ${}_n C_k = \binom{n}{k}$ |
//! | [`comb_rep`] | $k$-combinations with replacement, $\big(\\!\\!\binom{n}{k}\\!\\!\big)$ |
//! | [`perm`] | $k$-permutations of $n$ things, ${}_n P_k = \frac{n!}{(n-k)!}$ |
//! | [`stirling2`] | Stirling number of the second kind $S(n,k)$ |
//! | Function | Description |
//! | -------------- | ------------------------------------------------------------------------ |
//! | [`comb`] | $k$-combinations of $n$ things, $_nC_k = {n \choose k}$ |
//! | [`comb_rep`] | $k$-combinations with replacement, $\big(\\!\\!{n \choose k}\\!\\!\big)$ |
//! | [`perm`] | $k$-permutations of $n$ things, $_nP_k = {n! \over (n-k)!}$ |
//! | [`stirling2`] | Stirling number of the second kind $S(n,k)$ |
//!
//! # Factorials
//!
Expand Down Expand Up @@ -410,10 +410,10 @@
//!
//! | Function | Description |
//! | ------------- | ------------------------------------------------------------ |
//! | [`bernoulli`] | Bernoulli numbers $B_0, \ldots, B_{N-1}$ |
//! | [`bernoulli`] | Bernoulli numbers $B_0,\dotsc,B_{N-1}$ |
//! | [`binom`] | Binomial coefficient $\binom{n}{k}$ for real input |
//! | [`diric`] | Periodic sinc function, also called the Dirichlet kernel |
//! | [`euler`] | Euler numbers $E_0, \ldots, E_{N-1}$ |
//! | [`euler`] | Euler numbers $E_0,\dotsc,E_{N-1}$ |
//! | [`lambertw`] | Lambert W function, $W(z)$ |
//! | [`sici`] | Sine and cosine integrals $\Si(z)$ and $\Ci(z)$ |
//! | [`shichi`] | Hyperbolic sine and cosine integrals $\Shi(z)$ and $\Chi(z)$ |
Expand All @@ -440,8 +440,8 @@
//! | [`xlog1py`] | $x \ln(1+y)$ or $0$ if $x = 0$ |
//! | [`logaddexp`] | $\ln(e^x + e^y)$ |
//! | [`logaddexp2`] | $\log_2(2^x + 2^y)$ |
//! | [`exprel`] | Relative error exponential, $\frac{e^x - 1}{x}$ |
//! | [`sinc`] | Normalized sinc function, $\frac{\sin(\pi x)}{\pi x}$ |
//! | [`exprel`] | Relative error exponential, $e^x - 1 \over x$ |
//! | [`sinc`] | Normalized sinc function, $\sin(\pi x) \over \pi x$ |
//!
#![warn(
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6 changes: 3 additions & 3 deletions src/scipy_special/convex_analysis.rs
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Expand Up @@ -19,7 +19,7 @@
/// This function is concave.
///
/// The origin of this function is in convex programming [^1]. Given a discrete probability
/// distribution $p_1,\\, \ldots,\\, p_n$, the definition of entropy in the context of
/// distribution $p_1,\dotsc,p_n$, the definition of entropy in the context of
/// *information theory* is
///
/// $$
Expand Down Expand Up @@ -64,8 +64,8 @@ pub fn entr(x_i: f64) -> f64 {
/// This function is jointly convex in $x$ and $y$.
///
/// The origin of this function is in convex programming [^1]. Given two discrete probability
/// distributions $p_1,\\, \ldots,\\, p_n$ and $q_1,\\, \ldots,\\, q_n$, the definition of relative
/// entropy in the context of *information theory* is [^2]
/// distributions $p_1,\dotsc,p_n$ and $q_1,\dotsc,q_n$, the definition of relative entropy in the
/// context of *information theory* is [^2]
///
/// $$
/// H\left[ \\{ p_i \\} \\, \rvert \\, \\{ q_i \\} \right]
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48 changes: 20 additions & 28 deletions src/scipy_special/hypergeometric.rs
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Expand Up @@ -171,7 +171,7 @@ impl HypergeometricArg for num_complex::Complex<f64> {
}
}

/// Hypergeometric function $_0F_0\[\rvert\\,z\]$ for real or complex $z$
/// Hypergeometric function $_0F_0\left[\middle\| z\right]$ for real or complex $z$
///
/// This function is currently not implemented in SciPy, but is straightforward to evaluate.
/// Both [`f64`] and [`num_complex::Complex<f64>`](num_complex::Complex) are accepted for `z`.
Expand All @@ -181,24 +181,22 @@ impl HypergeometricArg for num_complex::Complex<f64> {
/// This function is defined as
///
/// $$
/// _0F_0\[\rvert\\,z\] = \sum\_{n=0}^\infty \frac{z^n}{n!} ,
/// _0F_0\left[ \middle\| z\right] = \sum\_{n=0}^\infty {z^n \over n!},
/// $$
///
/// which is just the exponential function, $e^z$.
///
/// # See also
/// - [`hyp1f0`]: Hypergeometric function $_1F_0\[a\\,\rvert\\,z\]$
/// - [`hyp0f1`]: Confluent hypergeometric limit function, $_0F_1\[b\\,\rvert\\,z\]$
/// - [`hyp1f1`](crate::hyp1f1): Kummer's confluent hypergeometric function,
/// $\hyp{1}{1}{a}{b}{\big\|\\,z}$
/// - [`hyp2f1`](crate::hyp2f1): Gauss' hypergeometric function,
/// $\hyp{2}{1}{a_1,\\ a_2}{b}{\big\|\\,z}$
/// - [`hyp1f0`]: Hypergeometric function $_1F_0\left[a\middle\| z\right]$
/// - [`hyp0f1`]: Confluent hypergeometric limit function, $_0F_1\left[b\middle\| z\right]$
/// - [`hyp1f1`](crate::hyp1f1): Kummer's confluent hypergeometric function, $\hyp 1 1 a b z$
/// - [`hyp2f1`](crate::hyp2f1): Gauss' hypergeometric function, $\hyp 2 1 {a_1\enspace a_2} b z$
///
pub fn hyp0f0<T: HypergeometricArg>(z: T) -> T {
z.hyp0f0()
}

/// Hypergeometric function $_1F_0\[a\\,\rvert\\,z\]$ for real or complex $z$
/// Hypergeometric function $_1F_0\left[a\middle\| z\right]$ for real or complex $z$
///
/// This function is currently not implemented in SciPy, but is straightforward to evaluate.
/// Both [`f64`] and [`num_complex::Complex<f64>`](num_complex::Complex) are accepted for `z`.
Expand All @@ -208,25 +206,23 @@ pub fn hyp0f0<T: HypergeometricArg>(z: T) -> T {
/// This function is defined as
///
/// $$
/// _1F_0\[a\\,\rvert\\,z\] = \sum\_{n=0}^\infty \rpow{a}{n} \frac{z^n}{n!}
/// _1F_0\left[a\middle\| z\right] = \sum\_{n=0}^\infty \rpow a n {z^n \over n!}
/// $$
///
/// Here $\rpow{\square}{n}$ is the rising factorial; see [`pow_rising`](crate::pow_rising).
/// Here $\rpow \square n$ is the rising factorial; see [`pow_rising`](crate::pow_rising).
/// It's also equal to $(1 - z)^{-a}$.
///
/// # See also
/// - [`hyp0f0`]: Hypergeometric function $_0F_0\[\rvert\\,z\]$
/// - [`hyp0f1`]: Confluent hypergeometric limit function, $_0F_1\[b\\,\rvert\\,z\]$
/// - [`hyp1f1`](crate::hyp1f1): Kummer's confluent hypergeometric function,
/// $\hyp{1}{1}{a}{b}{\big\|\\,z}$
/// - [`hyp2f1`](crate::hyp2f1): Gauss' hypergeometric function,
/// $\hyp{2}{1}{a_1,\\ a_2}{b}{\big\|\\,z}$
/// - [`hyp0f0`]: Hypergeometric function $_0F_0\left[\middle\| z\right]$
/// - [`hyp0f1`]: Confluent hypergeometric limit function, $_0F_1\left[b\middle\| z\right]$
/// - [`hyp1f1`](crate::hyp1f1): Kummer's confluent hypergeometric function, $\hyp 1 1 a b z$
/// - [`hyp2f1`](crate::hyp2f1): Gauss' hypergeometric function, $\hyp 2 1 {a_1\enspace a_2} b z$
///
pub fn hyp1f0<T: HypergeometricArg>(a: f64, z: T) -> T {
z.hyp1f0(a)
}

/// Confluent hypergeometric limit function $_0F_1\[b\\,\rvert\\,z\]$ for real or complex $z$
/// Confluent hypergeometric limit function $_0F_1\left[b\middle\| z\right]$ for real or complex $z$
///
/// This is a translation of the [`scipy.special.hyp0f1`][hyp0f1] Cython implementation into Rust,
/// using the same Cephes-based [scipy/xsf][xsf] FFI functions as SciPy.
Expand All @@ -239,22 +235,18 @@ pub fn hyp1f0<T: HypergeometricArg>(a: f64, z: T) -> T {
/// This function is defined as
///
/// $$
/// _0F_1\[b\\,\rvert\\,z\] = \sum\_{n=0}^\infty \frac{1}{\rpow{b}{n}} \frac{z^n}{n!}.
/// _0F_1\left[b\middle\| z\right] = \sum\_{n=0}^\infty {1\over \rpow b n} {z^n \over n!}.
/// $$
///
/// Here $\rpow{\square}{n}$ is the rising factorial; see [`pow_rising`](crate::pow_rising).
/// Here $\rpow \square n$ is the rising factorial; see [`pow_rising`](crate::pow_rising).
///
/// It's also the limit as $a \to \infty$ of $\hyp{1}{1}{a}{b}{\big\|\\,z}$, and satisfies the
/// It's also the limit as $a \to \infty$ of $\hyp 1 1 a b z$, and satisfies the
/// differential equation $f\'\'(z) + b f\'(z) = f(z)$. See [^1] for more information.
///
/// # See also
/// - [`hyp1f0`]: Hypergeometric function, $_1F_0\[a\\,\rvert\\,z\]$
/// - [`hyp1f1`](crate::hyp1f1): Kummer's confluent hypergeometric function,
/// $\hyp{1}{1}{a}{b}{\big\|\\,z}$
/// - [`hyp2f1`](crate::hyp2f1): Gauss' hypergeometric function,
/// $\hyp{2}{1}{a_1,\\ a_2}{b}{\big\|\\,z}$
/// - [`bessel_j`](crate::bessel_j): Bessel function of the first kind, $J_v(x)$
/// - [`bessel_i`](crate::bessel_i): Modified Bessel function of the first kind, $I_v(x)$
/// - [`hyp1f0`]: Hypergeometric function, $_1F_0\left[a\middle\| z\right]$
/// - [`hyp1f1`](crate::hyp1f1): Kummer's confluent hypergeometric function, $\hyp 1 1 a b z$
/// - [`hyp2f1`](crate::hyp2f1): Gauss' hypergeometric function, $\hyp 2 1 {a_1\enspace a_2} b z$
///
/// [^1]: Weisstein, Eric W. "Confluent Hypergeometric Limit Function." From MathWorld -- A Wolfram
/// Resource. <https://mathworld.wolfram.com/ConfluentHypergeometricLimitFunction.html>
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