# From the point (degrees) Creates a Spherical struct from three given points in space, with the angles in degrees. ``` # use scilib::coordinate::sp

# From the point (degrees) Creates a Cylindrical struct from three given points in space, with the angles in degrees. ``` # use scilib::coordinate::

# Radec coordinates from radians Generates the struct from angles given in radians. ## Inputs - `ra`: right ascension, in radians - `dec`: declinati

# Gaussian function ## Definition The [gaussian function](https://en.wikipedia.org/wiki/Gaussian_function) is a function defined as: $$ g(x) = a\cdot

# Generalized Legendre polynomials ## Definition Which can be generalized with a given derivative order $l$, following the formula: $$ P_n^l(x) = (-1

# Getting the coefficients of a polynomial Simply returns the HashMap of the power and associated coefficients. ``` # use std::collections::HashMap;

# Azimuthal quantum number $l$ The [azimuthal quantum number](https://en.wikipedia.org/wiki/Azimuthal_quantum_number) is computed based on the value o

# Magnetic quantum number $m$ The [magnetic quantum number](https://en.wikipedia.org/wiki/Magnetic_quantum_number) is computed based on the value of t

# Polynomial orders ## Definition Extracts the maximum order of the polynomial. Used built-in series function. ## Example ``` # use scilib::math::po

# Hermite polynomials ## Definitions The [Hermite polynomials](https://en.wikipedia.org/wiki/Hermite_polynomials) are a sequence of orthogonal polyno

# Exact Hill radius ## Definitions Similar to `hill_radius`, but solves the equation of the Hill radius: $$ \frac{m}{r_H^2} - \frac{M}{r^2}\left( 1 -

# Inverse fast Fourier transform Computes the IFFT for a one-dimensional array, based on the discrete Fourier transform. This function accepts comple

# Impact parameter $b$ ## Definition The impact parameter for an exoplanet orbiting a star is defined as: $$ b = \frac{a\cos(i)}{R_\mathrm{star}} \lef

# Polynomial integration ## Definition Computes the mth integration of the polynomial. Integration coefficients can be passed to the function, if an

# $J_n$ Bessel function (integer order) ## Definition The $J_n$ Bessel represent the first kind of Bessel function, and are solution to Bessel differ

# $K$ modified Bessel function ## Definition The $K$ modified Second Bessel function represent another kind of solution to the Bessel differential eq

# Kummer function ## Definition [Kummer function](https://en.wikipedia.org/wiki/Confluent_hypergeometric_function), is a generalized hypergeometric s

# Kurtosis of a series ## Definition We follow the mathematical definition of the kurtosis: $$ S = \left[\frac{1}{n} \sum_{i-1}^{n} \left( \frac{x_i

# Laguerre polynomials ## Definition The [Laguerre polynomials](https://en.wikipedia.org/wiki/Laguerre_polynomials) are the solution to the Laguerre

# Laplace distribution ## Definition The [Laplace distribution](https://en.wikipedia.org/wiki/Laplace_distribution) is a continuous probability distr

# Cumulative function of the Laplace distribution ## Definition The cumulative function for Laplace is defined by: $$ F_b(\mu, x) = \frac{1}{2} + \fr

# Legendre polynomials ## Definition The [Legendre polynomials](https://en.wikipedia.org/wiki/Legendre_polynomials) are used as solution to the Legen

# Levi-Civita symbol ## Definition $$ \epsilon_{ijk...l} $$ Computes the result of the $n$ dimensional Levi-Civita symbol. Returns 1 if the indexes a

# Polylogarithm ## Definition The [polylogarithm](https://en.wikipedia.org/wiki/Polylogarithm) is defined by the infinite series: $$ Li_s(z) = \sum_{

# Creating a logarithmic range from a number of points Creating a range with the start, stop, and number of points. If the range is invalid, an empty

# Logistic distribution ## Definition The [Logistic distribution](https://en.wikipedia.org/wiki/Logistic_distribution) is a continuous probability di

# Cumulative function of the Logistic distribution ## Definition The cumulative function for Logistic is defined by: $$ F_s(\mu, x) = \frac{1}{2} + \

# Luminosity using Stefan-Boltzmann ## Definition Computes the expected luminosity of a star using the Stefan-Boltzmann constant, from: $$ L = 4\pi\s

# Creates a new entity Returns the same value as `Self::default()`, all elements are equal to zero. ``` # use scilib::coordinate::spherical::Spheric

# Creates a new entity Returns the same value as `Self::default()`, all elements are equal to zero. ``` # use scilib::coordinate::cylindrical::Cylin

# Normal function ## Definition The [normal](https://en.wikipedia.org/wiki/Normal_distribution) is a continuous probability distribution. It is defin

# Cumulative function of the Normal distribution ## Definition The cumulative function for Normal is defined by: $$ F_\sigma(\mu, x) = \frac{1}{2}\le

# Orbital speed of an object ## Definition Computation for the velocity of an object on an elliptical orbit. The definition is: $$ v = \sqrt{GM\left(

# Creates a new entity Returns the same value as `Self::default()`, all elements are equal to zero. ``` # use scilib::coordinate::cartesian::Cartesi

# Builds Pascal's triangle line ## Definition We can obtain any given line of the [pascal triangle](https://en.wikipedia.org/wiki/Pascal%27s_triangle

# Maximum emission of a black body (frequency) ## Definition This is Wien's displacement law, applied to frequency: $$ \nu_\mathrm{peak} = b'T $$ Wher

# Maximum emission of a black body (wavelength) ## Definition This is Wien's displacement law, applied to wavelength: $$ \lambda_\mathrm{peak} = \frac

# Pearson r coefficient ## Definition The  is a correlation co

# Planetary luminosity ## Definition Computes the luminosity of a planet, based on the received irradiance and the albedo: $$ L_\mathrm{P} = E_\mathr

# Transit probability ## Definitions The probability is computed based on the occulted fraction of the line of longitude. Allowing for grazing eclips

# Radial wave-function for vectors Similar to `radial_wavefunction`, but computes the resulting values for a vector. This has the advantages to speed

# Radial wave-function Computes the result of the radial wave-function, as defined by: $$ R_n^l(r) = \sqrt{\left( \frac{2}{na_B} \right)^3 \frac{(n-l-

# Rayleigh distribution ## Definition The [Rayleigh distribution](https://en.wikipedia.org/wiki/Rayleigh_distribution) is a continuous probability di

# Rayleigh criterion ## Definition The Rayleigh criterion qualifies the minimum separation of two points that can be resolved as two distinct points b

# Cumulative function of the Rayleigh distribution ## Definition The cumulative function for Rayleigh is defined by: $$ F_\sigma(x) = 1 - \exp\left(-

# Energy received by an object ## Definition Computes the received energy by an object of a given surface, at a known distance. Makes use of the `irr

# Riccati-Bessel function $C_n$ ## Definition The $C_n$ Riccati-Bessel function is defined as: $$ C_n(z) = -\sqrt{\frac{\pi z}{2}}Y_{n+\frac{1}{2}}(z)

# Riccati-Bessel function $S_n$ ## Definition The $S_n$ Riccati-Bessel function is defined as: $$ S_n(z) = \sqrt{\frac{\pi z}{2}}J_{n+\frac{1}{2}}(z)

# Riccati-Bessel function $\xi_n$ ## Definition The $\xi_n$ Riccati-Bessel function is defined as: $$ \xi_n(z) = \sqrt{\frac{\pi z}{2}}H_{n+\frac{1}{2

# Riccati-Bessel function $\zeta_n$ ## Definition The $\zeta_n$ Riccati-Bessel function is defined as: $$ \zeta_n(z) = \sqrt{\frac{\pi z}{2}}H_{n+\fra

# Rising factorial ## Definition The [rising factorial](https://en.wikipedia.org/wiki/Falling_and_rising_factorials) is a polynomial, which can be co

# Coordinate rotation Computes the resulting coordinates after an arbitrary rotation in 3D. The rotation arguments are the yaw, pitch and roll in rad

# Min-Max scaling of a series ## Definition Min-Max scaling compresses all the data points passed in a series between two arbitrary values a and b. $

# Angular separation computation ## Definition We use the Vincenty formula to compute the angular separation, as it should remain stable no matter th

# First spherical Hankel function: $h^{(1)}$ ## Definition The first spherical hankel function is defined as: $$ h_n^{(1)}(x) = j_n(x) + iy_n(x) $$

# Second spherical Hankel function: $h^{(2)}$ ## Definition The second spherical hankel function is defined as: $$ h_n^{(2)}(x) = j_n(x) - iy_n(x) $$

# First spherical Hankel function (array): $h^{(1)}$ ## Inputs Compute the first kind of spherical hankel function by recurrence to get an array of f

# Second spherical Hankel function (array): $h^{(2)}$ ## Inputs Compute the second kind of spherical hankel function by recurrence to get an array of

# Sigmoid function ## Definition The [sigmoid function](https://en.wikipedia.org/wiki/Sigmoid_function) is defined as: $$ \sigma(x) = \frac{1}{1 + \e

# Sinus cardinal ## Definition The value of the [cardinal sinus](https://fr.wikipedia.org/wiki/Sinus_cardinal) is defined as: $$ \mathrm{sinc}(x) = \

# Skewness of a series ## Definition We follow the mathematical definition of the skewness: $$ S = \frac{1}{n} \sum_{i-1}^{n} \left( \frac{x_i - m}{\

# Specifying known distance Appends the distance to the Radec struct. ## Input - `distance`: distance of the object from earth, in meters ($m$) Retu

# Spherical harmonics Provides the solution to the angular $Y_l^m(\theta, \phi)$ wave-function: $$ Y_l^m(\theta, \phi) = (-1)^m \sqrt{\frac{(2l+1)}{4\

# Spherical harmonics for multiple angles theta

# Spin angular momentum The spin angular momentum $S$ is the quantized energy: $$ S = \hbar \sqrt{s(s+1)} = \frac{\hbar}{2}\sqrt{n(n+2)} $$ Where $\h

# Stirling number generator ## Definition The [Stirling numbers](https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind) are defined by the

# Signed Stirling number generator ## Definition The [signed Stirling numbers](https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind) have

# Student's t value ## Definition Computes the difference of means between two series. The $t$ value is simply defined as: $$ t = \frac{m_a - m_b}{s_

Full transit duration ## Definition The duration of the full transit, from the **end** of the ingress to the **start** of the egress. $$ T_{\mathrm{f

Total transit duration ## Definition The total duration of the transit, from the **start** of the ingress to the **end** of the egress. $$ T_{\mathrm

# Wavelength Planck's law ## Definition This computes the following equation: $$ B_\lambda(\lambda,T) = \frac{2hc^2}{\lambda^5} \frac{1}{\exp\left(\fr

# Wavelength Planck's law (spectrum) ## Definition This computes the following equation: $$ B_\lambda(\lambda,T) = \frac{2hc^2}{\lambda^5} \frac{1}{\e

# Wavenumber Planck's law ## Definition This computes the following equation: $$ B_{\tilde{n}}(\tilde{n},T) = 2hc^2\tilde{n}^3 \frac{1}{\exp\left(\fra

# Wavenumber Planck's law (spectrum) ## Definition This computes the following equation: $$ B_{\tilde{n}}(\tilde{n},T) = 2hc^2\tilde{n}^3 \frac{1}{\ex