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Decimal expansion of Pi^7.
9

%I #29 Aug 26 2024 05:02:07

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

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

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

%N Decimal expansion of Pi^7.

%C Wentworth (1903) shows how to compute the tangent of 15 degrees (A019913) to five decimal places by the laborious process of adding up the first few terms of Pi/12 + Pi^3/5184 + 2Pi^5/3732480 + 17Pi^7/11287019520 + ... - _Alonso del Arte_, Mar 13 2015

%D George Albert Wentworth, New Plane and Spherical Trigonometry, Surveying, and Navigation. Boston: The Atheneum Press (1903): 240.

%H G. C. Greubel, <a href="/A092735/b092735.txt">Table of n, a(n) for n = 4..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F From _Peter Bala_, Oct 30 2019: (Start)

%F Pi^7 = (6!/(2*33367)) * Sum_{n >= 0} (-1)^n*( 1/(n + 1/6)^7 + 1/(n + 5/6)^7 ), where 33367 = ((3^7 + 1)/4)*A000364(3) = A002437(3).

%F Pi^7 = (6!/(2*1191391)) * Sum_{n >= 0} (-1)^n*( 1/(n + 1/10)^7 - 1/(n + 3/10)^7 - 1/(n + 7/10)^7 + 1/(n + 9/10)^7 ), where 1191391 = ((5^7 - 1)/4)*A000364(3). (End)

%e 3020.293227776792067514206493...

%t RealDigits[Pi^7, 10, 100][[1]] (* _Alonso del Arte_, Mar 13 2015 *)

%o (PARI) Pi^7 \\ _G. C. Greubel_, Mar 09 2018

%o (Magma) R:= RealField(100); (Pi(R))^7; // _G. C. Greubel_, Mar 09 2018

%Y Cf. A000796, A002161, A019692, A091925, A092731, A000364, A002437.

%K cons,nonn

%O 4,1

%A _Mohammad K. Azarian_, Apr 12 2004