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A247719 Decimal expansion of Integral_{t=0..Pi/2} sqrt(tan(t)) dt. 10
2, 2, 2, 1, 4, 4, 1, 4, 6, 9, 0, 7, 9, 1, 8, 3, 1, 2, 3, 5, 0, 7, 9, 4, 0, 4, 9, 5, 0, 3, 0, 3, 4, 6, 8, 4, 9, 3, 0, 7, 3, 1, 0, 8, 4, 4, 6, 8, 7, 8, 4, 5, 1, 1, 1, 5, 4, 2, 6, 9, 7, 8, 0, 3, 4, 7, 8, 2, 1, 7, 3, 9, 6, 5, 4, 9, 7, 3, 6, 9, 5, 5, 2, 8, 7, 6, 6, 3, 4, 6, 7, 3, 8, 2, 3, 8, 2, 6, 1, 8, 6, 8, 1, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

D. H. Bailey, J. M. Borwein, Highly Parallel, High-Precision Numerical Integration p. 7. (2005) Lawrence Berkeley National Laboratory.

FORMULA

Equals Pi/sqrt(2).

Equals A063448/2.

c = 2*( Sum_{k >= 0} (-1)^k/(4*k + 1) + Sum_{k >= 0} (-1)^k/(4*k + 3) ) = 2*(A181048 + A181049). - Peter Bala, Sep 21 2016

From Amiram Eldar, Aug 07 2020: (Start)

Equals Integral_{x=0..Pi} 1/(cos(x)^2 + 1) dx = Integral_{x=0..Pi} 1/(sin(x)^2 + 1) dx.

Equals Integral_{x=-oo..oo} 1/(x^4 + 1) dx.

Equals Integral_{x=-oo..oo} x^2/(x^4 + 1) dx.

Equals Integral_{x=0..oo} log(1 + 1/(2 * x^2)) dx. (End)

EXAMPLE

2.22144146907918312350794049503034684930731...

MATHEMATICA

RealDigits[Pi/Sqrt[2], 10, 104] // First

PROG

(PARI) default(realprecision, 100); Pi/sqrt(2) \\ G. C. Greubel, Sep 07 2018

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)/Sqrt(2); // G. C. Greubel, Sep 07 2018

CROSSREFS

Cf. A063448, A093954, A193887, A244976, A181048, A181049.

Sequence in context: A105777 A014572 A071458 * A131308 A261360 A184242

Adjacent sequences:  A247716 A247717 A247718 * A247720 A247721 A247722

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Sep 23 2014

STATUS

approved

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Last modified January 27 11:43 EST 2021. Contains 340465 sequences. (Running on oeis4.)