Christoph Ruegg
11 years ago
3 changed files with 194 additions and 1 deletions
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Constants |
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========= |
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Math.NET Numerics contains a set of often used mathematical and scientific |
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constants. Mathematical and defined scientific constants are as accurate as |
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double precision allows, while measured constants are implemented according |
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to 2007 CODATA. |
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All constants are defined as static constant fields of the `Constants` class. |
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SI Unit Scaling |
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--------------- |
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Constant | Factor | Constant | Factor |
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-------- | --------- | -------- | ---------- |
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Deca | $10^{1}$ | Deci | $10^{-1}$ |
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Hecto | $10^{2}$ | Centi | $10^{-2}$ |
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Kilo | $10^{3}$ | Milli | $10^{-3}$ |
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Mega | $10^{6}$ | Micro | $10^{-6}$ |
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Giga | $10^{9}$ | Nano | $10^{-9}$ |
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Tera | $10^{12}$ | Pico | $10^{-12}$ |
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Peta | $10^{15}$ | Femto | $10^{-15}$ |
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Exa | $10^{18}$ | Atto | $10^{-18}$ |
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Zetta | $10^{21}$ | Zepto | $10^{-21}$ |
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Yotta | $10^{24}$ | Yocto | $10^{-24}$ |
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Mathematical Constants |
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---------------------- |
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Constant | Definition | Value (Rounded) |
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----------------- | ------------------------- | --------------- |
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E | $e$ | 2.7182818284590452354 |
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Log2E | $\log_2{e}$ | 1.4426950408889634074 |
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Log10E | $\log_{10}{e}$ | 0.4342944819032518277 |
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Ln2 | $\log_e{2}$ | 0.6931471805599453094 |
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Ln10 | $\log_e{10}$ | 2.3025850929940456840 |
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LnPi | $\log_e{\pi}$ | 1.1447298858494001741 |
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Ln2PiOver2 | $\frac{1}{2}\log_e{2\pi}$ | 0.9189385332046727418 |
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InvE | $\frac{1}{e}$ | 0.3678794411714423216 |
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SqrtE | $\sqrt{e}$ | 1.6487212707001281468 |
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Sqrt2 | $\sqrt{2}$ | 1.4142135623730950488 |
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Sqrt3 | $\sqrt{3}$ | 1.7320508075688772935 |
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Sqrt1Over2 | $\sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ | 0.7071067811865475244 |
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HalfSqrt3 | $\frac{1}{2}\sqrt{3}$ | 0.8660254037844386468 |
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Pi | $\pi$ | 3.1415926535897932385 |
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Pi2 | $2\pi$ | 6.2831853071795864769 |
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PiOver2 | $\frac{1}{2}\pi$ | 1.5707963267948966192 |
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Pi3Over2 | $\frac{3}{2}\pi$ | 4.7123889803846898577 |
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PiOver4 | $\frac{1}{4}\pi$ | 0.7853981633974483096 |
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SqrtPi | $\sqrt{\pi}$ | 1.7724538509055160273 |
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Sqrt2Pi | $\sqrt{2\pi}$ | 2.5066282746310005024 |
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Sqrt2PiE | $\sqrt{2\pi e}$ | 4.1327313541224929385 |
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LogSqrt2Pi | $\log_e{\sqrt{2\pi}} = \frac{1}{2}\log_e{2\pi}$ | 0.9189385332046727418 |
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LogSqrt2PiE | $\log_e{\sqrt{2\pi e}}$ | 1.4189385332046727418 |
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LogTwoSqrtEOverPi | $\log_e{2\sqrt{\frac{e}{\pi}}}$ | 0.6207822376352452223 |
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InvPi | $\frac{1}{\pi}$ | 0.3183098861837906715 |
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TwoInvPi | $\frac{2}{\pi}$ | 0.6366197723675813431 |
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InvSqrtPi | $\frac{1}{\sqrt{\pi}}$ | 0.5641895835477562869 |
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InvSqrt2Pi | $\frac{1}{\sqrt{2\pi}}$ | 0.3989422804014326779 |
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TwoInvSqrtPi | $\frac{2}{\sqrt{2\pi}}$ | 1.1283791670955125739 |
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TwoSqrtEOverPi | $2\sqrt{\frac{e}{\pi}}$ | 1.8603827342052657173 |
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Catalan | $\beta(2) = \sum_{k=0}^{\infty}{\frac{(-1)^k}{(2k+1)^2}}$ | 0.9159655941772190151 |
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EulerMascheroni | $\gamma = \lim_{n\to\infty} {\sum_{k=1}^n{(\frac{1}{k} - \log_e{n})}}$ | 0.5772156649015328606 |
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GoldenRatio | $\frac{1+\sqrt{5}}{2}$ | 1.6180339887498948482 |
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Glaisher | $\exp{(\frac{1}{12} - \zeta{(-1)})}$ | 1.2824271291006226369 |
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Khinchin | $K_0 = \prod_{k=1}^{\infty}{(1+\frac{1}{k(k+2)})^{\log_2{k}}}$ | 2.6854520010653064453 |
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Universal Constants |
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------------------- |
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Constant | Symbol | Unit | Value |
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----------------------------- | ------- | ------------- | ----- |
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SpeedOfLight | $c_0$ | $\frac{m}{s}$ | 2.99792458e+8 |
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MagneticPermeability | $\mu_0$ | $\frac{N}{A^2}$ = $\frac{kg\,m}{A^2s^2}$ | 1.2566370614359172954e-6 |
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ElectricPermittivity | $\varepsilon_0$ | $\frac{F}{m}$ = $\frac{A^2s^4}{kg\,m^3}$ | 8.8541878171937079245e-12 |
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CharacteristicImpedanceVacuum | $Z_0$ | $\Omega = \frac{kg\,m^2}{A^2s^3}$ | 376.7303134617706554682 |
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GravitationalConstant | $G$ | $\frac{m^3}{kg\,s^2}$ | 6.67429e-11 |
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PlancksConstant | $h$ | $J\,s = \frac{kg\,m^2}{s}$ | 6.62606896e-34 |
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DiracsConstant | $\hbar$ | $J\,s = \frac{kg\,m^2}{s}$ | 1.054571629e-34 |
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PlancksMass | $m_p$ | $kg$ | 2.17644e-8 |
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PlancksTemperature | $T_p$ | $K$ | 1.416786e+32 |
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PlancksLength | $l_p$ | $m$ | 1.616253e-35 |
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PlancksTime | $t_p$ | $s$ | 5.39124e-44 |
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Electromagnetic Constants |
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------------------------- |
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Constant | Symbol | Unit | Value |
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------------------- | ---------- | --------------------------------- | ----- |
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ElementaryCharge | $e$ | $C = A\,s$ | 1.602176487e-19 |
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MagneticFluxQuantum | $\Theta_0$ | $Wb = \frac{kg\,m^2}{A\,s^2}$ | 2.067833668e-15 |
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ConductanceQuantum | $G_0$ | $S = \frac{A^2s^3}{kg\,m^2}$ | 7.7480917005e-5 |
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JosephsonConstant | $K_J$ | $\frac{Hz}{V}$ | 483597.891e+9 |
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VonKlitzingConstant | $R_K$ | $\Omega = \frac{kg\,m^2}{A^2s^3}$ | 25812.807557 |
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BohrMagneton | $\mu_B$ | $\frac{J}{T}$ | 927.400915e-26 |
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NuclearMagneton | $\mu_N$ | $\frac{J}{T}$ | 5.05078324e-27 |
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Atomic and Nuclear Constants |
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---------------------------- |
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Constant | Symbol | Unit | Value |
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--------------------- | ------------ | ----------------- | ----- |
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FineStructureConstant | $\alpha$ | $1$ | 7.2973525376e-3 |
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RydbergConstant | $T_{\infty}$ | $\frac{1}{m}$ | 10973731.568528 |
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BohrRadius | $a_0$ | $m$ | 0.52917720859e-10 |
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HartreeEnergy | $E_h$ | $J$ | 4.35974394e-18 |
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QuantumOfCirculation | | $\frac{m^2}{s}$ | 3.6369475199e-4 |
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FermiCouplingConstant | | $\frac{1}{GeV^2}$ | 1.16637e-5 |
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WeakMixingAngle | | | 0.22256 |
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Avogadro | | $\frac{1}{mol}$ | 6.0221412927e23 |
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#### Electron |
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Constant | Unit | Value |
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---------------------------- | ---------------- | ----- |
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ElectronMass | $kg$ | 9.10938215e-31 |
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ElectronMassEnergyEquivalent | $J$ | 8.18710438e-14 |
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ElectronMolarMass | $\frac{kg}{mol}$ | 5.4857990943e-7 |
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ComptonWavelength | $m$ | 2.4263102175e-12 |
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ClassicalElectronRadius | $m$ | 2.8179402894e-15 |
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ThomsonCrossSection | $m^2$ | 0.6652458558e-28 |
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ElectronMagneticMoment | $\frac{J}{T}$ | -928.476377e-26 |
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ElectronGFactor | | -2.0023193043622 |
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#### Muon |
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Constant | Unit | Value |
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------------------------ | ---------------- | ----- |
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MuonMass | $kg$ | 1.88353130e-28 |
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MuonMassEnegryEquivalent | $J$ | 1.692833511e-11 |
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MuonMolarMass | $\frac{kg}{mol}$ | 0.1134289256e-3 |
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MuonComptonWavelength | $m$ | 11.73444104e-15 |
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MuonMagneticMoment | $\frac{J}{T}$ | -4.49044786e-26 |
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MuonGFactor | | -2.0023318414 |
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#### Tau |
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Constant | Unit | Value |
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----------------------- | ---------------- | ----- |
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TauMass | $kg$ | 3.16777e-27 |
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TauMassEnergyEquivalent | $J$ | 2.84705e-10 |
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TauMolarMass | $\frac{kg}{mol}$ | 1.90768e-3 |
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TauComptonWavelength | $m$ | 0.69772e-15 |
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#### Proton |
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Constant | Unit | Value |
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------------------------------- | ---------------- | ----- |
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ProtonMass | $kg$ | 1.672621637e-27 |
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ProtonMassEnergyEquivalent | $J$ | 1.503277359e-10 |
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ProtonMolarMass | $\frac{kg}{mol}$ | 1.00727646677e-3 |
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ProtonComptonWavelength | $m$ | 1.3214098446e-15 |
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ProtonMagneticMoment | $\frac{J}{T}$ | 1.410606662e-26 |
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ShieldedProtonMagneticMoment | $\frac{J}{T}$ | 1.410570419e-26 |
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ProtonGFactor | | 5.585694713 |
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ProtonGyromagneticRatio | $\frac{1}{T\,s}$ | 2.675222099e8 |
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ShieldedProtonGyromagneticRatio | $\frac{1}{T\,s}$ | 2.675153362e8 |
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#### Neutron |
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Constant | Unit | Value |
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--------------------------- | ---------------- | ----- |
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NeutronMass | $kg$ | 1.674927212e-27 |
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NeutronMassEnegryEquivalent | $J$ | 1.505349506e-10 |
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NeutronMolarMass | $\frac{kg}{mol}$ | 1.00866491597e-3 |
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NeutronComptonWavelength | $m$ | 1.3195908951e-1 |
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NeutronMagneticMoment | $\frac{J}{T}$ | -0.96623641e-26 |
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NeutronGFactor | | -3.82608545 |
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NeutronGyromagneticRatio | $\frac{1}{T\,s}$ | 1.83247185e8 |
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#### Deuteron |
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Constant | Unit | Value |
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---------------------------- | ---------------- | ----- |
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DeuteronMass | $kg$ | 3.34358320e-27 |
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DeuteronMassEnegryEquivalent | $J$ | 3.00506272e-10 |
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DeuteronMolarMass | $\frac{kg}{mol}$ | 2.013553212725e-3 |
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DeuteronMagneticMoment | $\frac{J}{T}$ | 0.433073465e-26 |
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#### Helion |
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Constant | Unit | Value |
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-------------------------- | ---------------- | ----- |
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HelionMass | $kg$ | 5.00641192e-27 |
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HelionMassEnegryEquivalent | $J$ | 4.49953864e-10 |
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HelionMolarMass | $\frac{kg}{mol}$ | 3.0149322473e-3 |
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