Table of constants with 50 decimal places
(Click here
for a for a Postscript version of this page and here
for a pdf version)
Here are given the first 50 decimal places of constants that occur
frequently in numerical computations (see also [1], [2]
and [4] for large tables of constants available on the
net). This number of digits should be enough for most practical purposes.
1 Related to p
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3.14159265358979323846264338327950288419716939937510... |
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1.57079632679489661923132169163975144209858469968755... |
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1.04719755119659774615421446109316762806572313312503... |
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0.78539816339744830961566084581987572104929234984377... |
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0.62831853071795864769252867665590057683943387987502... |
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0.52359877559829887307710723054658381403286156656251... |
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6.28318530717958647692528676655900576839433879875021... |
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9.42477796076937971538793014983850865259150819812531... |
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12.56637061435917295385057353311801153678867759750042... |
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9.86960440108935861883449099987615113531369940724079... |
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31.00627668029982017547631506710139520222528856588510... |
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0.31830988618379067153776752674502872406891929148091... |
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0.63661977236758134307553505349005744813783858296182... |
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1.77245385090551602729816748334114518279754945612238... |
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0.56418958354775628694807945156077258584405062932899... |
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2.50662827463100050241576528481104525300698674060993... |
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0.39894228040143267793994605993438186847585863116493... |
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1.46459188756152326302014252726379039173859685562793... |
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2 Related to e
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2.71828182845904523536028747135266249775724709369995... |
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1.35914091422952261768014373567633124887862354684997... |
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5.43656365691809047072057494270532499551449418739991... |
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7.38905609893065022723042746057500781318031557055184... |
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20.08553692318766774092852965458171789698790783855415... |
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0.36787944117144232159552377016146086744581113103176... |
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1.64872127070012814684865078781416357165377610071014... |
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0.60653065971263342360379953499118045344191813548718... |
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23.14069263277926900572908636794854738026610624260021... |
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0.04321391826377224977441773717172801127572810981063... |
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4.81047738096535165547303566670383312639017087466453... |
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0.20787957635076190854695561983497877003387784163176... |
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1.78107241799019798523650410310717954916964521430343... |
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0.56145948356688516982414321479088078676571038692515... |
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15.15426224147926418976043027262991190552854853685613... |
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0.065988035845312537076790187596846424938577048252796... |
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3 Related to Catalan's constant
G is defined by the series expansion
G= |
¥ å
n=0
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(-1)n
(2n+1)2
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0.91596559417721901505460351493238411077414937428167... |
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1.09174406370390610145415947333389232498605012140824... |
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0.29156090403081878013838445646839491886406615398583... |
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3.42981513013245864263455323784799901211670795530093... |
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4 Square roots
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1.41421356237309504880168872420969807856967187537694... |
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1.73205080756887729352744634150587236694280525381038... |
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2.23606797749978969640917366873127623544061835961152... |
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2.64575131106459059050161575363926042571025918308245... |
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3.16227766016837933199889354443271853371955513932521... |
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0.70710678118654752440084436210484903928483593768847... |
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0.57735026918962576450914878050195745564760175127012... |
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0.44721359549995793928183473374625524708812367192230... |
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1.61803398874989484820458683436563811772030917980576... |
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1.25992104989487316476721060727822835057025146470150... |
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1.18920711500272106671749997056047591529297209246381... |
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2.66514414269022518865029724987313984827421131371465... |
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f = 1/2+Ö5/2 is the golden ratio.
5 Logarithms
We define the logarithm as :
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0.69314718055994530941723212145817656807550013436025... |
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1.09861228866810969139524523692252570464749055782274... |
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1.60943791243410037460075933322618763952560135426851... |
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1.94591014905531330510535274344317972963708472958186... |
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2.30258509299404568401799145468436420760110148862877... |
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0.43429448190325182765112891891660508229439700580366... |
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0.63092975357145743709952711434276085429958564013188... |
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-0.36651292058166432701243915823266946945426344783711... |
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1.14472988584940017414342735135305871164729481291531... |
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0.91893853320467274178032973640561763986139747363778... |
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-0.54953931298164482233766176880290778833069898126306... |
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0.48121182505960344749775891342436842313518433438566... |
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6 Gamma and Psi functions
An elementary definition is :
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ó õ
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¥
0
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tx-1e-tdt, with x > 0, |
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and we have the important relations
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0.57721566490153286060651209008240243104215933593992... |
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1.73245471460063347358302531586082968115577655226680... |
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1.77245385090551602729816748334114518279754945612238... |
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2.67893853470774763365569294097467764412868937795730... |
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1.35411793942640041694528802815451378551932726605679... |
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3.62560990822190831193068515586767200299516768288006... |
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1.22541670246517764512909830336289052685123924810807... |
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1.46163214496836234126265954232572132846819620400644... |
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0.88560319441088870027881590058258873320795153366990... |
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-1.96351002602142347944097633299875556719315960466043... |
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-3.13203378002080632299641907428726885415542829672041... |
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-1.31823441578658847240234081664511312187136204862767... |
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-4.22745353337626540808953014609668357736724443870824... |
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-1.08586087978647216962688676281718069317007503933313... |
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5.24411510858423962092967917978223882736550990286325... |
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L is the Lemniscate constant and its value is given by
7 Riemann Zeta function
For any s > 1
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1.64493406684822643647241516664602518921894990120679... |
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1.20205690315959428539973816151144999076498629234049... |
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1.08232323371113819151600369654116790277475095191872... |
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1.03692775514336992633136548645703416805708091950191... |
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1.01734306198444913971451792979092052790181749003285... |
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-1.46035450880958681288949915251529801246722933101258... |
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-0.97336024835078271546888686244789657077282963174305... |
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-2.44758073623365823109099570422300521301545223575799... |
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2.61237534868548834334856756792407163057080065240006... |
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-0.20788622497735456601730672539704930222626853128767... |
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0.607927101854026628663276779258365833426152648033479... |
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-0.91893853320467274178032973640561763986139747363778... |
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-0.93754825431584375370257409456786497789786028861482... |
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7.1 Non trivial zeros
First roots of the equation z(s)=0 of the form
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14.13472514173469379045725198356247027078425711569924... |
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21.02203963877155499262847959389690277733434052490278... |
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25.01085758014568876321379099256282181865954967255799... |
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30.42487612585951321031189753058409132018156002371544... |
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32.93506158773918969066236896407490348881271560351703... |
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37.58617815882567125721776348070533282140559735083079... |
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You may find very complete tables on the zeros of the Riemann zeta function
at [3].
8 Number theory
In this section the letter p always denotes a prime and the sums or
products are only involving the set of prime numbers.
- Mertens constant M
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lim
n® ¥
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æ è
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å
p £ n
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1
p
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-log(log(n)) |
ö ø
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0.26149721284764278375542683860869585905156664826119... |
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- Artin's constant
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Õ
p ³ 2
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æ è
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1- |
1
p(p-1)
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ö ø
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0.37395581361920228805472805434641641511162924860615... |
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- Twin prime constant
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Õ
p ³ 3
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æ è
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1- |
1
(p-1)2
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ö ø
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0.66016181584686957392781211001455577843262336028473... |
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1.32032363169373914785562422002911155686524672056946... |
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- Landau-Ramanujan constant
K=0.76422365358922066299069873125009232811679054139340... |
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References
- [1]
- M. Abramowitz and I. Stegun, Handbook of
Mathematical Functions, Dover, New York, (1964)
- [2]
- D.E. Knuth, The Art of Computer Programming, Vol.
II, Seminumerical Algorithms, Addison Wesley, (1998)
- [3]
- A. Odlyzko, Tables of zeros of the Riemann zeta
function, http://www.dtc.umn.edu/~odlyzko/
- [4]
- S. Plouffe, Plouffe's Inverter,
http://pi.lacim.uqam.ca/eng/
File translated from
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version 3.01.
On 22 Nov 2002, 14:34.