A256192 -id:A256192 - cp's OEIS frontend

A257955 Decimal expansion of Gamma(1/Pi).

2, 8, 1, 1, 2, 9, 7, 5, 1, 4, 6, 7, 0, 8, 6, 1, 6, 4, 2, 1, 2, 2, 7, 9, 0, 8, 0, 3, 7, 1, 0, 4, 8, 1, 6, 9, 3, 5, 2, 8, 1, 6, 5, 5, 2, 2, 3, 2, 9, 1, 7, 6, 5, 6, 8, 2, 2, 8, 9, 6, 5, 9, 0, 5, 3, 9, 3, 8, 6, 1, 5, 4, 8, 8, 7, 0, 1, 9, 2, 0, 5, 6, 8, 5, 1, 8, 8, 4, 8, 7, 4, 2, 3, 1, 8, 9, 0, 9, 3, 6, 4, 2, 4

Offset: 1

Iaroslav V. Blagouchine, May 14 2015

The reference gives an interesting product representation in terms of rational multiple of 1/Pi for Gamma(1/Pi).

			2.8112975146708616421227908037104816935281655223291765...

G. C. Greubel, Table of n, a(n) for n = 1..5000
Iaroslav V. Blagouchine, Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to 1/Pi, Mathematics of Computation (AMS), 2015.

Cf. A257957, A257958, A257959, A002161, A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

Maple
```
evalf(GAMMA(1/Pi), 117);
```
Mathematica
```
RealDigits[Gamma[1/Pi], 10, 117][[1]]
```

default(realprecision, 117); gamma(1/Pi)

A269545 Decimal expansion of Gamma(Pi).

Original entry on oeis.org

2, 2, 8, 8, 0, 3, 7, 7, 9, 5, 3, 4, 0, 0, 3, 2, 4, 1, 7, 9, 5, 9, 5, 8, 8, 9, 0, 9, 0, 6, 0, 2, 3, 3, 9, 2, 2, 8, 8, 9, 6, 8, 8, 1, 5, 3, 3, 5, 6, 2, 2, 2, 4, 4, 1, 1, 9, 9, 3, 8, 0, 7, 4, 5, 4, 7, 0, 4, 7, 1, 0, 0, 6, 6, 0, 8, 5, 0, 4, 2, 8, 2, 5, 0, 0, 7, 2, 5, 3, 0, 4, 4, 6, 7, 9, 2, 8, 4, 7, 4, 7, 9, 6

Offset: 1

Iaroslav V. Blagouchine, Feb 29 2016

			2.2880377953400324179595889090602339228896881533562224...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A269546, A269547, A269557, A269558, A269559, A257955, A257957, A257958, A257959, A002161, A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

MATLAB
```
format long; gamma(pi)
```
Maple
```
evalf(GAMMA(Pi), 120);
```
Mathematica
```
RealDigits[Gamma[Pi], 10, 120][[1]]
```
PARI
```
default(realprecision, 120); gamma(Pi)
```

Equals Integral_{x >= 0} x^(Pi-1)/e^x dx (Euler integral of the second kind).

A269546 Decimal expansion of log(Gamma(Pi)).

Original entry on oeis.org

8, 2, 7, 6, 9, 4, 5, 9, 2, 3, 2, 3, 4, 3, 7, 1, 0, 1, 5, 2, 9, 5, 7, 8, 5, 5, 8, 4, 5, 2, 3, 5, 9, 9, 5, 1, 1, 5, 3, 5, 0, 1, 7, 3, 4, 1, 2, 0, 7, 3, 7, 3, 1, 6, 7, 9, 1, 3, 1, 9, 2, 2, 5, 8, 1, 7, 1, 9, 3, 5, 7, 7, 1, 9, 7, 6, 9, 1, 7, 1, 4, 1, 8, 3, 1, 5, 7, 5, 1, 6, 1, 8, 0, 5, 5, 1, 8, 7, 5, 3, 6, 0, 5

Offset: 0

Iaroslav V. Blagouchine, Feb 29 2016

Gamma(x) is the Gamma function (Euler's integral of the second kind).

			0.8276945923234371015295785584523599511535017341207373...

G. C. Greubel, Table of n, a(n) for n = 0..5000

Cf. A269545, A269547, A269557, A269558, A269559, A257955, A257957, A257958, A257959, A002161.

Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

MATLAB
```
format long; log(gamma(pi))
```
Maple
```
evalf(lnGAMMA(Pi), 120);
```
Mathematica
```
RealDigits[LogGamma[Pi], 10, 120][[1]]
```

default(realprecision, 120); lngamma(Pi)

A269547 Decimal expansion of Psi(Pi).

Original entry on oeis.org

9, 7, 7, 2, 1, 3, 3, 0, 7, 9, 4, 2, 0, 0, 6, 7, 3, 3, 2, 9, 2, 0, 6, 9, 4, 8, 6, 4, 0, 6, 1, 8, 2, 3, 4, 3, 6, 4, 0, 8, 3, 4, 6, 0, 9, 9, 9, 4, 3, 2, 5, 6, 3, 8, 0, 0, 9, 5, 2, 3, 2, 8, 6, 5, 3, 1, 8, 1, 0, 5, 9, 2, 4, 7, 7, 7, 1, 4, 1, 3, 1, 7, 3, 0, 2, 0, 7, 5, 6, 5, 4, 3, 6, 2, 9, 2, 8, 7, 3, 4, 3, 5, 5

Offset: 0

Iaroslav V. Blagouchine, Feb 29 2016

Psi(x) is the digamma function (logarithmic derivative of the Gamma function).

			0.9772133079420067332920694864061823436408346099943256...

G. C. Greubel, Table of n, a(n) for n = 0..5000

Cf. A269545, A269546, A269557, A269558, A269559, A257955, A257957, A257958, A257959, A002161.

Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

MATLAB
```
format long; psi(pi)
```
Maple
```
evalf(Psi(Pi), 120)
```
Mathematica
```
RealDigits[PolyGamma[Pi], 10, 120][[1]]
```
PARI
```
default(realprecision, 120); psi(Pi)
```

A269557 Decimal expansion of Gamma(log(2)).

Original entry on oeis.org

1, 3, 0, 9, 0, 4, 0, 9, 1, 1, 2, 8, 1, 4, 8, 1, 2, 6, 9, 8, 2, 4, 5, 3, 2, 5, 2, 1, 3, 9, 5, 9, 2, 9, 5, 7, 5, 6, 1, 2, 5, 8, 9, 0, 3, 1, 9, 1, 8, 1, 8, 9, 0, 0, 1, 0, 3, 8, 9, 8, 0, 0, 0, 7, 9, 0, 9, 0, 9, 3, 9, 7, 6, 3, 4, 5, 6, 3, 2, 7, 4, 7, 1, 6, 0, 9, 7, 4, 1, 2, 5, 0, 3, 0, 1, 0, 0, 4, 3, 5, 1, 0, 5

Offset: 1

Iaroslav V. Blagouchine, Feb 29 2016

Gamma(x) is the Gamma function (Euler's integral of the second kind).

			1.3090409112814812698245325213959295756125890319181890...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A269558, A269559, A269545, A269546, A269547, A257955, A257957, A257958, A257959, A002161.

Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

MATLAB
```
format long; gamma(log(2))
```
Maple
```
evalf(GAMMA(ln(2)), 120);
```
Mathematica
```
RealDigits[Gamma[Log[2]], 10, 120][[1]]
```

default(realprecision, 120); gamma(log(2))

A269558 Decimal expansion of log(Gamma(log(2))).

Original entry on oeis.org

2, 6, 9, 2, 9, 4, 7, 4, 0, 2, 8, 3, 1, 3, 1, 2, 4, 2, 9, 4, 9, 9, 1, 6, 5, 8, 3, 2, 1, 1, 7, 1, 2, 8, 2, 4, 8, 8, 8, 9, 0, 3, 5, 1, 0, 2, 1, 1, 1, 6, 6, 1, 1, 7, 2, 8, 7, 0, 6, 1, 3, 1, 8, 9, 6, 9, 4, 8, 4, 9, 8, 7, 1, 3, 5, 9, 1, 1, 6, 0, 3, 2, 8, 0, 6, 2, 1, 6, 1, 5, 3, 6, 0, 2, 4, 6, 3, 8, 0, 9, 3, 0, 5

Offset: 0

Iaroslav V. Blagouchine, Feb 29 2016

Gamma(x) is the Gamma function (Euler's integral of the second kind).

			0.2692947402831312429499165832117128248889035102111661...

G. C. Greubel, Table of n, a(n) for n = 0..5000

Cf. A269557, A269559, A269545, A269546, A269547, A257955, A257957, A257958, A257959, A002161.

Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

MATLAB
```
format long; log(gamma(log(2)))
```
Maple
```
evalf(lnGAMMA(ln(2)), 120);
```

RealDigits[LogGamma[Log[2]], 10, 120][[1]]

default(realprecision, 120); lngamma(log(2))

A269559 Decimal expansion of Psi(log(2)), negated.

Original entry on oeis.org

1, 2, 3, 9, 5, 9, 7, 2, 7, 9, 6, 1, 7, 6, 1, 8, 5, 0, 8, 2, 4, 4, 1, 2, 7, 5, 5, 1, 6, 8, 6, 0, 8, 4, 2, 4, 5, 4, 3, 3, 2, 8, 9, 5, 2, 2, 6, 8, 7, 4, 2, 0, 8, 6, 6, 4, 6, 1, 6, 4, 8, 9, 8, 8, 8, 1, 9, 4, 0, 6, 3, 8, 9, 3, 3, 4, 5, 3, 5, 9, 0, 1, 5, 8, 7, 3, 2, 6, 0, 6, 9, 4, 5, 7, 3, 4, 8, 8, 2, 3, 8, 2, 0

Offset: 1

Iaroslav V. Blagouchine, Feb 29 2016

Psi(x) is the digamma function (logarithmic derivative of the Gamma function).

			-1.2395972796176185082441275516860842454332895226874208...

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A269557, A269558, A269545, A269546, A269547, A257955, A257957, A257958, A257959, A002161.

Cf. A073005, A068466, A175380, A175379, A220086, A203142, A256190, A256191, A256192, A203140, A203139, A203138, A203137.

MATLAB
```
format long; psi(log(2))
```
Maple
```
evalf(Psi(ln(2)), 120);
```

RealDigits[PolyGamma[Log[2]], 10, 120][[1]]

default(realprecision, 120); psi(log(2))

A020014 Nearest integer to Gamma(n + 1/11)/Gamma(1/11).

Original entry on oeis.org

1, 0, 0, 0, 1, 3, 13, 81, 577, 4665, 42405, 427909, 4745900, 57382240, 751185683, 10584889175, 159735600270, 2570291022522, 43928610203109, 794708493674422, 15171707606511701, 304813398276280545, 6428791672736098775

Offset: 0

Simon Plouffe

nonn

			Gamma(n + 1/11)/Gamma(1/11) = 1, 1/11, 12/121, 276/1331, 9384/14641, 422280/161051, 23647680/1771561, ... - _R. J. Mathar_, Sep 04 2016

G. C. Greubel, Table of n, a(n) for n = 0..450

Cf. A020059, A020104, A010680 (decimal expansion of 1/11), A256192 (decimal expansion of Gamma(1/11)).

[Round(Gamma(n +1/11)/Gamma(1/11)): n in [0..30]]; // G. C. Greubel, Jan 19 2018

f := proc(n) round(simplify(GAMMA(n+1/11)/GAMMA(1/11))); end:
map(f, [$0..60]); # Edited by Robert Israel, Mar 25 2018

Table[Round[Gamma[n + 1/11]/Gamma[1/11]], {n, 0,50}] (* G. C. Greubel, Jan 19 2018 *)

for(n=0,30, print1(round(gamma(n+1/11)/gamma(1/11)), ", ")) \\ G. C. Greubel, Jan 19 2018

cp's OEIS Frontend

A257955 Decimal expansion of Gamma(1/Pi).

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A269545 Decimal expansion of Gamma(Pi).

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A269546 Decimal expansion of log(Gamma(Pi)).

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A269547 Decimal expansion of Psi(Pi).

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A269557 Decimal expansion of Gamma(log(2)).

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MATLAB

Maple

Mathematica

PARI

A269558 Decimal expansion of log(Gamma(log(2))).

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

MATLAB

Maple

Mathematica

PARI

A269559 Decimal expansion of Psi(log(2)), negated.

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