Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Replace TeX escape sequences with unicode counterparts #487

Open
wants to merge 1 commit into
base: master
Choose a base branch
from
Open
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
16 changes: 8 additions & 8 deletions docs/src/functions_overview.md
Original file line number Diff line number Diff line change
Expand Up @@ -8,15 +8,15 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi

| Function | Description |
|:-------- |:----------- |
| [`gamma(z)`](@ref SpecialFunctions.gamma(::Number)) | [gamma function](https://en.wikipedia.org/wiki/Gamma_function) ``\Gamma(z)`` |
| [`gamma(z)`](@ref SpecialFunctions.gamma(::Number)) | [gamma function](https://en.wikipedia.org/wiki/Gamma_function) ``Γ(z)`` |
| [`loggamma(x)`](@ref SpecialFunctions.loggamma(::Number)) | accurate `log(gamma(x))` for large `x` |
| [`logabsgamma(x)`](@ref SpecialFunctions.logabsgamma) | accurate `log(abs(gamma(x)))` for large `x` |
| [`logfactorial(x)`](@ref SpecialFunctions.logfactorial) | accurate `log(factorial(x))` for large `x`; same as `loggamma(x+1)` for `x > 1`, zero otherwise |
| [`digamma(x)`](@ref SpecialFunctions.digamma) | [digamma function](https://en.wikipedia.org/wiki/Digamma_function) (i.e. the derivative of `loggamma` at `x`) |
| [`invdigamma(x)`](@ref SpecialFunctions.invdigamma) | [invdigamma function](http://bariskurt.com/calculating-the-inverse-of-digamma-function/) (i.e. inverse of `digamma` function at `x` using fixed-point iteration algorithm) |
| [`trigamma(x)`](@ref SpecialFunctions.trigamma) | [trigamma function](https://en.wikipedia.org/wiki/Trigamma_function) (i.e the logarithmic second derivative of `gamma` at `x`) |
| [`polygamma(m,x)`](@ref SpecialFunctions.polygamma) | [polygamma function](https://en.wikipedia.org/wiki/Polygamma_function) (i.e the (m+1)-th derivative of the `loggamma` function at `x`) |
| [`gamma(a,z)`](@ref SpecialFunctions.gamma(::Number,::Number)) | [upper incomplete gamma function ``\Gamma(a,z)``](https://en.wikipedia.org/wiki/Incomplete_gamma_function) |
| [`gamma(a,z)`](@ref SpecialFunctions.gamma(::Number,::Number)) | [upper incomplete gamma function ``Γ(a,z)``](https://en.wikipedia.org/wiki/Incomplete_gamma_function) |
| [`loggamma(a,z)`](@ref SpecialFunctions.loggamma(::Number,::Number)) | accurate `log(gamma(a,x))` for large arguments |
| [`gamma_inc(a,x,IND)`](@ref SpecialFunctions.gamma_inc) | [incomplete gamma function ratio P(a,x) and Q(a,x)](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates P(a,x) and Q(a,x) for accuracy specified by IND and returns tuple (p,q)) |
| [`gamma_inc_inv(a,p,q)`](@ref SpecialFunctions.gamma_inc_inv) | [inverse of incomplete gamma function ratio P(a,x) and Q(a,x)](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates x given P(a,x)=p and Q(a,x)=q) |
Expand All @@ -34,11 +34,11 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi

| Function | Description |
|:-------- |:----------- |
| [`expint(ν, z)`](@ref SpecialFunctions.expint) | [exponential integral](https://en.wikipedia.org/wiki/Exponential_integral) ``\operatorname{E}_\nu(z)`` |
| [`expinti(x)`](@ref SpecialFunctions.expinti) | [exponential integral](https://en.wikipedia.org/wiki/Exponential_integral) ``\operatorname{Ei}(x)`` |
| [`expintx(x)`](@ref SpecialFunctions.expintx) | scaled [exponential integral](https://en.wikipedia.org/wiki/Exponential_integral) ``e^z \operatorname{E}_\nu(z)`` |
| [`sinint(x)`](@ref SpecialFunctions.sinint) | [sine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Sine_integral) ``\operatorname{Si}(x)`` |
| [`cosint(x)`](@ref SpecialFunctions.cosint) | [cosine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Cosine_integral) ``\operatorname{Ci}(x)`` |
| [`expint(ν, z)`](@ref SpecialFunctions.expint) | [exponential integral](https://en.wikipedia.org/wiki/Exponential_integral) ``\operatorname{E}(z)`` |
| [`expinti(x)`](@ref SpecialFunctions.expinti) | [exponential integral](https://en.wikipedia.org/wiki/Exponential_integral) ``\operatorname{Ei}(x)`` |
| [`expintx(x)`](@ref SpecialFunctions.expintx) | scaled [exponential integral](https://en.wikipedia.org/wiki/Exponential_integral) ``e^z \operatorname{E}(z)`` |
| [`sinint(x)`](@ref SpecialFunctions.sinint) | [sine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Sine_integral) ``\operatorname{Si}(x)`` |
| [`cosint(x)`](@ref SpecialFunctions.cosint) | [cosine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Cosine_integral) ``\operatorname{Ci}(x)`` |


## Error Functions, Dawson’s and Fresnel Integrals
Expand All @@ -56,7 +56,7 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
| [`logerfcx(x)`](@ref SpecialFunctions.logerfcx) | log of the scaled complementary error function, i.e. accurate ``\operatorname{ln}(\operatorname{erfcx}(x))`` for large negative ``x`` |
| [`erfi(x)`](@ref SpecialFunctions.erfi) | imaginary error function defined as ``-i \operatorname{erf}(ix)`` |
| [`erfinv(x)`](@ref SpecialFunctions.erfinv) | inverse function to [`erf()`](@ref SpecialFunctions.erf) |
| [`dawson(x)`](@ref SpecialFunctions.dawson) | scaled imaginary error function, a.k.a. Dawson function, i.e. accurate ``\frac{\sqrt{\pi}}{2} e^{-x^2} \operatorname{erfi}(x)`` for large ``x`` |
| [`dawson(x)`](@ref SpecialFunctions.dawson) | scaled imaginary error function, a.k.a. Dawson function, i.e. accurate ``\frac{\sqrt{π}}{2} e^{-x^2} \operatorname{erfi}(x)`` for large ``x`` |
| [`faddeeva(x)`](@ref SpecialFunctions.faddeeva) | [Faddeeva function](https://en.wikipedia.org/wiki/Faddeeva_function), equivalent to ``\operatorname{erfcx}(-ix)`` |


Expand Down
26 changes: 13 additions & 13 deletions src/bessel.jl
Original file line number Diff line number Diff line change
Expand Up @@ -465,7 +465,7 @@ end
@doc raw"""
besseli(nu, x)

Modified Bessel function of the first kind of order `nu`, ``I_\nu(x)``.
Modified Bessel function of the first kind of order `nu`, ``I_ν(x)``.

External links:
[DLMF 10.25.2](https://dlmf.nist.gov/10.25.2),
Expand All @@ -486,7 +486,7 @@ end
@doc raw"""
besselix(nu, x)

Scaled modified Bessel function of the first kind of order `nu`, ``I_\nu(x) e^{- | \operatorname{Re}(x) |}``.
Scaled modified Bessel function of the first kind of order `nu`, ``I_ν(x) e^{- | \operatorname{Re}(x) |}``.

External links:
[DLMF 10.25.2](https://dlmf.nist.gov/10.25.2),
Expand All @@ -507,7 +507,7 @@ end
@doc raw"""
besselj(nu, x)

Bessel function of the first kind of order `nu`, ``J_\nu(x)``.
Bessel function of the first kind of order `nu`, ``J_ν(x)``.

External links:
[DLMF 10.2.2](https://dlmf.nist.gov/10.2.2),
Expand All @@ -532,7 +532,7 @@ end
@doc raw"""
besseljx(nu, x)

Scaled Bessel function of the first kind of order `nu`, ``J_\nu(x) e^{- | \operatorname{Im}(x) |}``.
Scaled Bessel function of the first kind of order `nu`, ``J_ν(x) e^{- | \operatorname{Im}(x) |}``.

External links:
[DLMF 10.2.2](https://dlmf.nist.gov/10.2.2),
Expand All @@ -553,7 +553,7 @@ end
@doc raw"""
besselk(nu, x)

Modified Bessel function of the second kind of order `nu`, ``K_\nu(x)``.
Modified Bessel function of the second kind of order `nu`, ``K_ν(x)``.

External links:
[DLMF 10.25.3](https://dlmf.nist.gov/10.25.3),
Expand All @@ -576,7 +576,7 @@ end
@doc raw"""
besselkx(nu, x)

Scaled modified Bessel function of the second kind of order `nu`, ``K_\nu(x) e^x``.
Scaled modified Bessel function of the second kind of order `nu`, ``K_ν(x) e^x``.

External links:
[DLMF 10.25.3](https://dlmf.nist.gov/10.25.3),
Expand All @@ -599,7 +599,7 @@ end
"""
bessely(nu, x)

Bessel function of the second kind of order `nu`, ``Y_\\nu(x)``.
Bessel function of the second kind of order `nu`, ``Y_ν(x)``.

External links:
[DLMF 10.2.3](https://dlmf.nist.gov/10.2.3),
Expand All @@ -620,7 +620,7 @@ end
besselyx(nu, x)

Scaled Bessel function of the second kind of order `nu`,
``Y_\\nu(x) e^{- | \\operatorname{Im}(x) |}``.
``Y_ν(x) e^{- | \\operatorname{Im}(x) |}``.

External links:
[DLMF 10.2.3](https://dlmf.nist.gov/10.2.3),
Expand Down Expand Up @@ -784,7 +784,7 @@ sphericalbessely(nu, x::T) where {T} = √((float(T))(π)/2x) * bessely(nu + one
"""
hankelh1(nu, x)

Bessel function of the third kind of order `nu`, ``H^{(1)}_\\nu(x)``.
Bessel function of the third kind of order `nu`, ``H^{(1)}(x)``.

External links:
[DLMF 10.2.5](https://dlmf.nist.gov/10.2.5),
Expand All @@ -797,7 +797,7 @@ hankelh1(nu, z) = besselh(nu, 1, z)
"""
hankelh2(nu, x)

Bessel function of the third kind of order `nu`, ``H^{(2)}_\\nu(x)``.
Bessel function of the third kind of order `nu`, ``H^{(2)}(x)``.

External links:
[DLMF 10.2.6](https://dlmf.nist.gov/10.2.6),
Expand All @@ -810,7 +810,7 @@ hankelh2(nu, z) = besselh(nu, 2, z)
"""
hankelh1x(nu, x)

Scaled Bessel function of the third kind of order `nu`, ``H^{(1)}_\\nu(x) e^{-x i}``.
Scaled Bessel function of the third kind of order `nu`, ``H^{(1)}(x) e^{-x i}``.

External links:
[DLMF 10.2.5](https://dlmf.nist.gov/10.2.5),
Expand All @@ -823,7 +823,7 @@ hankelh1x(nu, z) = besselhx(nu, 1, z)
@doc raw"""
hankelh2x(nu, x)

Scaled Bessel function of the third kind of order `nu`, ``H^{(2)}_\nu(x) e^{x i}``.
Scaled Bessel function of the third kind of order `nu`, ``H^{(2)}(x) e^{x i}``.

External links:
[DLMF 10.2.6](https://dlmf.nist.gov/10.2.6),
Expand All @@ -839,7 +839,7 @@ hankelh2x(nu, z) = besselhx(nu, 2, z)
Bessel function of the first kind divided by `x`.
Following convention:
```math
\operatorname{jinc}{x} = \frac{2 J_1({\pi x})}{\pi x}.
\operatorname{jinc}{x} = \frac{2 J_1({π x})}{π x}.
```
Sometimes known as sombrero or besinc function.

Expand Down
16 changes: 8 additions & 8 deletions src/beta_inc.jl
Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@ const exparg_p = log(prevfloat(floatmax(Float64)))
@doc raw"""
loggammadiv(a,b)

Computes ``\log(\Gamma(b)/\Gamma(a+b))`` when `b >= 8`
Computes ``\log(Γ(b)/Γ(a+b))`` when `b >= 8`
"""
loggammadiv(a::Number, b::Number) = _loggammadiv(promote(float(a), float(b))...)

Expand Down Expand Up @@ -76,7 +76,7 @@ end
@doc raw"""
esum(mu,x)

Compute ``e^{\mu+x}``
Compute ``e^{μ+x}``
"""
function esum(mu::Float64, x::Float64)
if x > 0.0
Expand All @@ -95,7 +95,7 @@ end
@doc raw"""
beta_integrand(a, b, x, y, mu=0.0)

Compute ``e^{\mu} x^a y^b / B(a,b)``
Compute ``e^{μ} x^a y^b / B(a,b)``
"""
function beta_integrand(a::Float64, b::Float64, x::Float64, y::Float64, mu::Float64=0.0)
a0, b0 = minmax(a,b)
Expand Down Expand Up @@ -181,7 +181,7 @@ end
beta_inc_cont_fraction(a,b,x,y,lambda,epps)

Compute ``I_{x}(a,b)`` using continued fraction expansion when `a, b > 1`.
It is assumed that ``\lambda = (a+b)*y - b``
It is assumed that ``λ = (a+b)*y - b``

External links:
[DLMF 8.17.22](https://dlmf.nist.gov/8.17.22),
Expand Down Expand Up @@ -251,7 +251,7 @@ end
beta_inc_asymptotic_symmetric(a,b,lambda,epps)

Compute ``I_{x}(a,b)`` using asymptotic expansion for `a, b >= 15`.
It is assumed that ``\lambda = (a+b)*y - b``.
It is assumed that ``λ = (a+b)*y - b``.

External links:
[DLMF 8.17.22](https://dlmf.nist.gov/8.17.22),
Expand Down Expand Up @@ -525,7 +525,7 @@ end

Computes ``I_x(a,b)`` using power series:
```math
I_{x}(a,b) = G(a,b) x^{a}/a \left[1 + a \sum_{j=1}^{\infty} ((1-b)(2-b)\dots(j-b)/j!(a+j)) x^{j}\right]
I_{x}(a,b) = G(a,b) x^{a}/a \left[1 + a \sum_{j=1}^ ((1-b)(2-b)\dots(j-b)/j!(a+j)) x^{j}\right]
```
External links:
[DLMF 8.17.22](https://dlmf.nist.gov/8.17.22),
Expand Down Expand Up @@ -733,9 +733,9 @@ end
Return a tuple ``(I_{x}(a,b), 1-I_{x}(a,b))`` where ``I_{x}(a,b)`` is the regularized
incomplete beta function given by
```math
I_{x}(a,b) = \frac{1}{B(a,b)} \int_{0}^{x} t^{a-1}(1-t)^{b-1} \mathrm{d}t,
I_{x}(a,b) = \frac{1}{B(a,b)} \int_0^x t^{a-1}(1-t)^{b-1} \mathrm{d}t,
```
where ``B(a,b) = \Gamma(a)\Gamma(b)/\Gamma(a+b)``.
where ``B(a,b) = Γ(a)Γ(b)/Γ(a+b)``.

External links:
[DLMF 8.17.1](https://dlmf.nist.gov/8.17.1),
Expand Down
22 changes: 11 additions & 11 deletions src/betanc.jl
Original file line number Diff line number Diff line change
Expand Up @@ -10,9 +10,9 @@ const errmax = 1e-15
Compute tail of the noncentral beta distribution.
Uses the recursive relation
```math
I_{x}(a,b+1;0) = I_{x}(a,b;0) - \Gamma(a+b)/\Gamma(a+1)\Gamma(b) x^a (1-x)^b
I_{x}(a,b+1;0) = I_{x}(a,b;0) - Γ(a+b)/Γ(a+1)Γ(b) x^a (1-x)^b
```
and ``\Gamma(a+1) = a\Gamma(a)`` given in [DLMF 8.17.21](https://dlmf.nist.gov/8.17.21).
and ``Γ(a+1) = (a)`` given in [DLMF 8.17.21](https://dlmf.nist.gov/8.17.21).
"""
function ncbeta_tail(a::Float64, b::Float64, lambda::Float64, x::Float64)
if x <= 0.0
Expand Down Expand Up @@ -55,16 +55,16 @@ end
ncbeta_poisson(a,b,lambda,x)

Compute CDF of noncentral beta if `lambda >= 54` using:
First ``\lambda/2`` is calculated and the Poisson term is calculated using
``P(j-1) = j/\lambda P(j)`` and ``P(j+1) = \lambda/(j+1) P(j)``.
First ``λ/2`` is calculated and the Poisson term is calculated using
``P(j-1) = j/λ P(j)`` and ``P(j+1) = λ/(j+1) P(j)``.
Then backward recurrences are used until either the Poisson weights fall below
`errmax` or `iterlo` is reached.
```math
I_{x}(a+j-1,b) = I_{x}(a+j,b) + \Gamma(a+b+j-1)/\Gamma(a+j)\Gamma(b)x^{a+j-1}(1-x)^{b}
I_{x}(a+j-1,b) = I_{x}(a+j,b) + Γ(a+b+j-1)/Γ(a+j)Γ(b) x^{a+j-1} (1-x)^{b}
```
Then forward recurrences are used until error bound falls below `errmax`.
```math
I_{x}(a+j+1,b) = I_{x}(a+j,b) - \Gamma(a+b+j)/\Gamma(a+j)\Gamma(b)x^{a+j}(1-x)^{b}
I_{x}(a+j+1,b) = I_{x}(a+j,b) - Γ(a+b+j)/Γ(a+j)Γ(b) x^{a+j} (1-x)^{b}
```
"""
function ncbeta_poisson(a::Float64, b::Float64, lambda::Float64, x::Float64)
Expand Down Expand Up @@ -147,10 +147,10 @@ end

Compute the CDF of the noncentral beta distribution given by
```math
I_{x}(a,b; \lambda) = \sum_{j=0}^{\infty} q(\lambda/2,j) I_{x}(a+j,b;0)
I_{x}(a,b; λ) = \sum_{j=0}^ q(λ/2,j) I_{x}(a+j,b;0)
```
For ``\lambda < 54`` : algorithm suggested by Lenth(1987) in `ncbeta_tail(a,b,lambda,x)`.
Else for ``\lambda \geq 54``: modification in Chattamvelli(1997) in
For ``λ < 54`` : algorithm suggested by Lenth(1987) in `ncbeta_tail(a,b,lambda,x)`.
Else for ``λ ≥ 54``: modification in Chattamvelli(1997) in
`ncbeta_poisson(a,b,lambda,x)` by using both forward and backward recurrences.
"""
function ncbeta(a::Float64, b::Float64, lambda::Float64, x::Float64)
Expand All @@ -173,9 +173,9 @@ end

Compute CDF of noncentral F distribution given by:
```math
F(x, v_1, v_2; \lambda) = I_{v_1 x/(v_1 x + v_2)}(v_1/2, v_2/2; \lambda)
F(x, v_1, v_2; λ) = I_{v_1 x/(v_1 x + v_2)}(v_1/2, v_2/2; λ)
```
where ``I_{x}(a,b; \lambda)`` is the noncentral beta function computed above.
where ``I_{x}(a,b; λ)`` is the noncentral beta function computed above.

External links:
[Wikipedia](https://en.wikipedia.org/wiki/Noncentral_F-distribution)
Expand Down
20 changes: 10 additions & 10 deletions src/ellip.jl
Original file line number Diff line number Diff line change
Expand Up @@ -11,8 +11,8 @@ Computes Complete Elliptic Integral of 1st kind ``K(m)`` for parameter ``m`` giv
```math
\operatorname{ellipk}(m)
= K(m)
= \int_0^{ \frac{\pi}{2} } \frac{1}{\sqrt{1 - m \sin^2 \theta}} \, \mathrm{d}\theta
\quad \text{for} \quad m \in \left( -\infty, 1 \right] \, .
= \int_0^{ \frac{π}{2} } \frac{1}{\sqrt{1 - m \sin^2 θ}} \, \mathrm{d}θ
\quad \text{for} \quad m \in \left( -, 1 \right] \, .
```

External links:
Expand All @@ -22,9 +22,9 @@ External links:
See also: [`ellipe(m)`](@ref SpecialFunctions.ellipe).

# Arguments
- `m`: parameter ``m``, restricted to the domain ``(-\infty,1]``, is related to
- `m`: parameter ``m``, restricted to the domain ``(-,1]``, is related to
the elliptic modulus ``k`` by ``k^2=m`` and to the modular angle
``\alpha`` by ``k = \sin \alpha``.
``α`` by ``k = \sin α``.

# Implementation
Using piecewise approximation polynomial as given in
Expand All @@ -40,7 +40,7 @@ For ``m<0``, followed by
> Journal of Computational and Applied Mathematics. 282.
> DOI 10.13140/2.1.1946.6245.,
> <https://www.researchgate.net/publication/267330394>
As suggested in this paper, the domain is restricted to ``(-\infty,1]``.
As suggested in this paper, the domain is restricted to ``(-,1]``.
"""
ellipk(m::Real) = _ellipk(float(m))

Expand Down Expand Up @@ -191,8 +191,8 @@ Computes Complete Elliptic Integral of 2nd kind ``E(m)`` for parameter ``m`` giv
```math
\operatorname{ellipe}(m)
= E(m)
= \int_0^{ \frac{\pi}{2} } \sqrt{1 - m \sin^2 \theta} \, \mathrm{d}\theta
\quad \text{for} \quad m \in \left( -\infty, 1 \right] .
= \int_0^{ \frac{π}{2} } \sqrt{1 - m \sin^2 θ} \, \mathrm{d}θ
\quad \text{for} \quad m \in \left( -, 1 \right] .
```

External links:
Expand All @@ -202,9 +202,9 @@ External links:
See also: [`ellipk(m)`](@ref SpecialFunctions.ellipk).

# Arguments
- `m`: parameter ``m``, restricted to the domain ``(-\infty,1]``, is related to
- `m`: parameter ``m``, restricted to the domain ``(-,1]``, is related to
the elliptic modulus ``k`` by ``k^2=m`` and to the modular angle
``\alpha`` by ``k=\sin \alpha``.
``α`` by ``k = \sin α``.

# Implementation
Using piecewise approximation polynomial as given in
Expand All @@ -220,7 +220,7 @@ For ``m<0``, followed by
> Journal of Computational and Applied Mathematics. 282.
> DOI 10.13140/2.1.1946.6245.,
> <https://www.researchgate.net/publication/267330394>
As suggested in this paper, the domain is restricted to ``(-\infty,1]``.
As suggested in this paper, the domain is restricted to ``(-,1]``.
"""
ellipe(m::Real) = _ellipe(float(m))

Expand Down
8 changes: 4 additions & 4 deletions src/erf.jl
Original file line number Diff line number Diff line change
Expand Up @@ -82,7 +82,7 @@ end
Compute the error function of ``x``, defined by

```math
\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x \exp(-t^2) \; \mathrm{d}t
\operatorname{erf}(x) = \frac{2}{\sqrt{π}} \int_0^x \exp(-t^2) \; \mathrm{d}t
\quad \text{for} \quad x \in \mathbb{C} \, .
```

Expand Down Expand Up @@ -126,7 +126,7 @@ Compute the complementary error function of ``x``, defined by
```math
\operatorname{erfc}(x)
= 1 - \operatorname{erf}(x)
= \frac{2}{\sqrt{\pi}} \int_x^\infty \exp(-t^2) \; \mathrm{d}t
= \frac{2}{\sqrt{π}} \int_x^ \exp(-t^2) \; \mathrm{d}t
\quad \text{for} \quad x \in \mathbb{C} \, .
```

Expand Down Expand Up @@ -200,11 +200,11 @@ Compute the Dawson function (scaled imaginary error function) of ``x``, defined

```math
\operatorname{dawson}(x)
= \frac{\sqrt{\pi}}{2} e^{-x^2} \operatorname{erfi}(x)
= \frac{\sqrt{π}}{2} e^{-x^2} \operatorname{erfi}(x)
\quad \text{for} \quad x \in \mathbb{C} \, .
```

This is the accurate version of ``\frac{\sqrt{\pi}}{2} e^{-x^2} \operatorname{erfi}(x)``
This is the accurate version of ``\frac{\sqrt{π}}{2} e^{-x^2} \operatorname{erfi}(x)``
for large ``x``.

External links: [DLMF 7.2.5](https://dlmf.nist.gov/7.2.5),
Expand Down
Loading
Loading