|
| |
|
|
A092735
|
|
Decimal expansion of Pi^7.
|
|
8
|
|
|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
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 A302244
Adjacent sequences: A092732 A092733 A092734 * A092736 A092737 A092738
|
|
|
KEYWORD
|
cons,nonn
|
|
|
AUTHOR
|
Mohammad K. Azarian, Apr 12 2004
|
|
|
STATUS
|
approved
|
| |
|
|
