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

4,1

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

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

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).

Cf. A019692, A091925 and A092731. (End)

Example

3020.293227776792067514206493...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A059339 A241181 A171772 * A035464 A194669 A364570

Adjacent sequences: A092732 A092733 A092734 * A092736 A092737 A092738

Keyword

cons,nonn

Author

Mohammad K. Azarian, Apr 12 2004

Status

approved