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