A092735 Decimal expansion of Pi^7.

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, 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, 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

Offset: 4

Author

Mohammad K. Azarian, Apr 12 2004

Keywords

• cons
• nonn

Comments

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

Examples

			3020.293227776792067514206493...
		

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 4..10000
• Index entries for transcendental numbers

Crossrefs

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

Programs

Magma

R:= RealField(100); (Pi(R))^7; // G. C. Greubel, Mar 09 2018

Mathematica

RealDigits[Pi^7, 10, 100][[1]] (* Alonso del Arte, Mar 13 2015 *)

PARI

Pi^7 \\ G. C. Greubel, Mar 09 2018

Formula

From Peter Bala, Oct 30 2019: (Start)

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).

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)