login
Decimal expansion of Integral_{0..Pi/2} exp(t)*cos(t) dt.
1

%I #19 Sep 08 2022 08:46:09

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

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

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

%N Decimal expansion of Integral_{0..Pi/2} exp(t)*cos(t) dt.

%H G. C. Greubel, <a href="/A247718/b247718.txt">Table of n, a(n) for n = 1..10000</a>

%H D. H. Bailey, J. M. Borwein, <a href="https://escholarship.org/uc/item/4281090t">Highly Parallel, High-Precision Numerical Integration</a> p. 6. (2005) Lawrence Berkeley National Laboratory.

%F Equals (A042972 - 1)/2 = A097666 -1/2, where A042972 is exp(Pi/2).

%e 1.90523869048267582773651783335191656319508543733226747...

%t RealDigits[(Exp[Pi/2] - 1)/2, 10, 105] // First

%o (PARI) default(realprecision, 100); (exp(Pi/2) -1)/2 \\ _G. C. Greubel_, Sep 07 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Exp(Pi(R)/2) - 1)/2; // _G. C. Greubel_, Sep 07 2018

%Y Cf. A042972.

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Sep 23 2014