diff --git a/MathNet.Numerics.sln b/MathNet.Numerics.sln index 2aecf100..58787f08 100644 --- a/MathNet.Numerics.sln +++ b/MathNet.Numerics.sln @@ -36,6 +36,7 @@ Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "Docs", "Docs", "{039229DA-A ProjectSection(SolutionItems) = preProject docs\content\Build.md = docs\content\Build.md docs\content\Compatibility.md = docs\content\Compatibility.md + docs\content\Constants.md = docs\content\Constants.md docs\content\CSV.md = docs\content\CSV.md docs\content\DescriptiveStatistics.md = docs\content\DescriptiveStatistics.md docs\content\Distance.md = docs\content\Distance.md diff --git a/docs/content/Constants.md b/docs/content/Constants.md new file mode 100644 index 00000000..62d9bf66 --- /dev/null +++ b/docs/content/Constants.md @@ -0,0 +1,191 @@ +Constants +========= + +Math.NET Numerics contains a set of often used mathematical and scientific +constants. Mathematical and defined scientific constants are as accurate as +double precision allows, while measured constants are implemented according +to 2007 CODATA. + +All constants are defined as static constant fields of the `Constants` class. + + +SI Unit Scaling +--------------- + +Constant | Factor | Constant | Factor +-------- | --------- | -------- | ---------- +Deca | $10^{1}$ | Deci | $10^{-1}$ +Hecto | $10^{2}$ | Centi | $10^{-2}$ +Kilo | $10^{3}$ | Milli | $10^{-3}$ +Mega | $10^{6}$ | Micro | $10^{-6}$ +Giga | $10^{9}$ | Nano | $10^{-9}$ +Tera | $10^{12}$ | Pico | $10^{-12}$ +Peta | $10^{15}$ | Femto | $10^{-15}$ +Exa | $10^{18}$ | Atto | $10^{-18}$ +Zetta | $10^{21}$ | Zepto | $10^{-21}$ +Yotta | $10^{24}$ | Yocto | $10^{-24}$ + + +Mathematical Constants +---------------------- + +Constant | Definition | Value (Rounded) +----------------- | ------------------------- | --------------- +E | $e$ | 2.7182818284590452354 +Log2E | $\log_2{e}$ | 1.4426950408889634074 +Log10E | $\log_{10}{e}$ | 0.4342944819032518277 +Ln2 | $\log_e{2}$ | 0.6931471805599453094 +Ln10 | $\log_e{10}$ | 2.3025850929940456840 +LnPi | $\log_e{\pi}$ | 1.1447298858494001741 +Ln2PiOver2 | $\frac{1}{2}\log_e{2\pi}$ | 0.9189385332046727418 +InvE | $\frac{1}{e}$ | 0.3678794411714423216 +SqrtE | $\sqrt{e}$ | 1.6487212707001281468 +Sqrt2 | $\sqrt{2}$ | 1.4142135623730950488 +Sqrt3 | $\sqrt{3}$ | 1.7320508075688772935 +Sqrt1Over2 | $\sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ | 0.7071067811865475244 +HalfSqrt3 | $\frac{1}{2}\sqrt{3}$ | 0.8660254037844386468 +Pi | $\pi$ | 3.1415926535897932385 +Pi2 | $2\pi$ | 6.2831853071795864769 +PiOver2 | $\frac{1}{2}\pi$ | 1.5707963267948966192 +Pi3Over2 | $\frac{3}{2}\pi$ | 4.7123889803846898577 +PiOver4 | $\frac{1}{4}\pi$ | 0.7853981633974483096 +SqrtPi | $\sqrt{\pi}$ | 1.7724538509055160273 +Sqrt2Pi | $\sqrt{2\pi}$ | 2.5066282746310005024 +Sqrt2PiE | $\sqrt{2\pi e}$ | 4.1327313541224929385 +LogSqrt2Pi | $\log_e{\sqrt{2\pi}} = \frac{1}{2}\log_e{2\pi}$ | 0.9189385332046727418 +LogSqrt2PiE | $\log_e{\sqrt{2\pi e}}$ | 1.4189385332046727418 +LogTwoSqrtEOverPi | $\log_e{2\sqrt{\frac{e}{\pi}}}$ | 0.6207822376352452223 +InvPi | $\frac{1}{\pi}$ | 0.3183098861837906715 +TwoInvPi | $\frac{2}{\pi}$ | 0.6366197723675813431 +InvSqrtPi | $\frac{1}{\sqrt{\pi}}$ | 0.5641895835477562869 +InvSqrt2Pi | $\frac{1}{\sqrt{2\pi}}$ | 0.3989422804014326779 +TwoInvSqrtPi | $\frac{2}{\sqrt{2\pi}}$ | 1.1283791670955125739 +TwoSqrtEOverPi | $2\sqrt{\frac{e}{\pi}}$ | 1.8603827342052657173 +Catalan | $\beta(2) = \sum_{k=0}^{\infty}{\frac{(-1)^k}{(2k+1)^2}}$ | 0.9159655941772190151 +EulerMascheroni | $\gamma = \lim_{n\to\infty} {\sum_{k=1}^n{(\frac{1}{k} - \log_e{n})}}$ | 0.5772156649015328606 +GoldenRatio | $\frac{1+\sqrt{5}}{2}$ | 1.6180339887498948482 +Glaisher | $\exp{(\frac{1}{12} - \zeta{(-1)})}$ | 1.2824271291006226369 +Khinchin | $K_0 = \prod_{k=1}^{\infty}{(1+\frac{1}{k(k+2)})^{\log_2{k}}}$ | 2.6854520010653064453 + + +Universal Constants +------------------- + +Constant | Symbol | Unit | Value +----------------------------- | ------- | ------------- | ----- +SpeedOfLight | $c_0$ | $\frac{m}{s}$ | 2.99792458e+8 +MagneticPermeability | $\mu_0$ | $\frac{N}{A^2}$ = $\frac{kg\,m}{A^2s^2}$ | 1.2566370614359172954e-6 +ElectricPermittivity | $\varepsilon_0$ | $\frac{F}{m}$ = $\frac{A^2s^4}{kg\,m^3}$ | 8.8541878171937079245e-12 +CharacteristicImpedanceVacuum | $Z_0$ | $\Omega = \frac{kg\,m^2}{A^2s^3}$ | 376.7303134617706554682 +GravitationalConstant | $G$ | $\frac{m^3}{kg\,s^2}$ | 6.67429e-11 +PlancksConstant | $h$ | $J\,s = \frac{kg\,m^2}{s}$ | 6.62606896e-34 +DiracsConstant | $\hbar$ | $J\,s = \frac{kg\,m^2}{s}$ | 1.054571629e-34 +PlancksMass | $m_p$ | $kg$ | 2.17644e-8 +PlancksTemperature | $T_p$ | $K$ | 1.416786e+32 +PlancksLength | $l_p$ | $m$ | 1.616253e-35 +PlancksTime | $t_p$ | $s$ | 5.39124e-44 + + +Electromagnetic Constants +------------------------- + +Constant | Symbol | Unit | Value +------------------- | ---------- | --------------------------------- | ----- +ElementaryCharge | $e$ | $C = A\,s$ | 1.602176487e-19 +MagneticFluxQuantum | $\Theta_0$ | $Wb = \frac{kg\,m^2}{A\,s^2}$ | 2.067833668e-15 +ConductanceQuantum | $G_0$ | $S = \frac{A^2s^3}{kg\,m^2}$ | 7.7480917005e-5 +JosephsonConstant | $K_J$ | $\frac{Hz}{V}$ | 483597.891e+9 +VonKlitzingConstant | $R_K$ | $\Omega = \frac{kg\,m^2}{A^2s^3}$ | 25812.807557 +BohrMagneton | $\mu_B$ | $\frac{J}{T}$ | 927.400915e-26 +NuclearMagneton | $\mu_N$ | $\frac{J}{T}$ | 5.05078324e-27 + + +Atomic and Nuclear Constants +---------------------------- + +Constant | Symbol | Unit | Value +--------------------- | ------------ | ----------------- | ----- +FineStructureConstant | $\alpha$ | $1$ | 7.2973525376e-3 +RydbergConstant | $T_{\infty}$ | $\frac{1}{m}$ | 10973731.568528 +BohrRadius | $a_0$ | $m$ | 0.52917720859e-10 +HartreeEnergy | $E_h$ | $J$ | 4.35974394e-18 +QuantumOfCirculation | | $\frac{m^2}{s}$ | 3.6369475199e-4 +FermiCouplingConstant | | $\frac{1}{GeV^2}$ | 1.16637e-5 +WeakMixingAngle | | | 0.22256 +Avogadro | | $\frac{1}{mol}$ | 6.0221412927e23 + +#### Electron + +Constant | Unit | Value +---------------------------- | ---------------- | ----- +ElectronMass | $kg$ | 9.10938215e-31 +ElectronMassEnergyEquivalent | $J$ | 8.18710438e-14 +ElectronMolarMass | $\frac{kg}{mol}$ | 5.4857990943e-7 +ComptonWavelength | $m$ | 2.4263102175e-12 +ClassicalElectronRadius | $m$ | 2.8179402894e-15 +ThomsonCrossSection | $m^2$ | 0.6652458558e-28 +ElectronMagneticMoment | $\frac{J}{T}$ | -928.476377e-26 +ElectronGFactor | | -2.0023193043622 + +#### Muon + +Constant | Unit | Value +------------------------ | ---------------- | ----- +MuonMass | $kg$ | 1.88353130e-28 +MuonMassEnegryEquivalent | $J$ | 1.692833511e-11 +MuonMolarMass | $\frac{kg}{mol}$ | 0.1134289256e-3 +MuonComptonWavelength | $m$ | 11.73444104e-15 +MuonMagneticMoment | $\frac{J}{T}$ | -4.49044786e-26 +MuonGFactor | | -2.0023318414 + +#### Tau + +Constant | Unit | Value +----------------------- | ---------------- | ----- +TauMass | $kg$ | 3.16777e-27 +TauMassEnergyEquivalent | $J$ | 2.84705e-10 +TauMolarMass | $\frac{kg}{mol}$ | 1.90768e-3 +TauComptonWavelength | $m$ | 0.69772e-15 + +#### Proton + +Constant | Unit | Value +------------------------------- | ---------------- | ----- +ProtonMass | $kg$ | 1.672621637e-27 +ProtonMassEnergyEquivalent | $J$ | 1.503277359e-10 +ProtonMolarMass | $\frac{kg}{mol}$ | 1.00727646677e-3 +ProtonComptonWavelength | $m$ | 1.3214098446e-15 +ProtonMagneticMoment | $\frac{J}{T}$ | 1.410606662e-26 +ShieldedProtonMagneticMoment | $\frac{J}{T}$ | 1.410570419e-26 +ProtonGFactor | | 5.585694713 +ProtonGyromagneticRatio | $\frac{1}{T\,s}$ | 2.675222099e8 +ShieldedProtonGyromagneticRatio | $\frac{1}{T\,s}$ | 2.675153362e8 + +#### Neutron + +Constant | Unit | Value +--------------------------- | ---------------- | ----- +NeutronMass | $kg$ | 1.674927212e-27 +NeutronMassEnegryEquivalent | $J$ | 1.505349506e-10 +NeutronMolarMass | $\frac{kg}{mol}$ | 1.00866491597e-3 +NeutronComptonWavelength | $m$ | 1.3195908951e-1 +NeutronMagneticMoment | $\frac{J}{T}$ | -0.96623641e-26 +NeutronGFactor | | -3.82608545 +NeutronGyromagneticRatio | $\frac{1}{T\,s}$ | 1.83247185e8 + +#### Deuteron + +Constant | Unit | Value +---------------------------- | ---------------- | ----- +DeuteronMass | $kg$ | 3.34358320e-27 +DeuteronMassEnegryEquivalent | $J$ | 3.00506272e-10 +DeuteronMolarMass | $\frac{kg}{mol}$ | 2.013553212725e-3 +DeuteronMagneticMoment | $\frac{J}{T}$ | 0.433073465e-26 + +#### Helion + +Constant | Unit | Value +-------------------------- | ---------------- | ----- +HelionMass | $kg$ | 5.00641192e-27 +HelionMassEnegryEquivalent | $J$ | 4.49953864e-10 +HelionMolarMass | $\frac{kg}{mol}$ | 3.0149322473e-3 diff --git a/docs/tools/templates/template.cshtml b/docs/tools/templates/template.cshtml index ce5d05d9..dab8c13e 100644 --- a/docs/tools/templates/template.cshtml +++ b/docs/tools/templates/template.cshtml @@ -83,7 +83,7 @@
  • Getting started
  • -
  • Constants
  • +
  • Constants
  • Floating-Point Numbers
  • Arbitrary Precision Numbers
  • Complex Numbers
  • @@ -93,6 +93,7 @@
  • Special Functions
  • +
  • Differentiation
  • Integration