A346571 -id:A346571 - cp's OEIS frontend

A346570 Decimal expansion of 2 - 33367 * Pi^7 / 100776960.

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

Offset: 0

Sean A. Irvine, Jul 23 2021

			0.9999884484387282478381315723917964998588...

L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (316).

Michael I. Shamos, Shamos's catalog of the real numbers (2011).
Index entries for transcendental numbers.

Cf. A346573, A346572, A346571, A346449, A346450.

RealDigits[2 - 33367 * Pi^7 / 100776960, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

Equals 2 - 61 * 547 * Pi^7 / (2^10 * 3^9 * 5).

Equals 1 + Sum_{k>=1} ( ((-1)^k/(6*k-1)^7 - (-1)^k/(6*k+1)^7) ).

A346572 Decimal expansion of 2 - 7 * Pi^3 / 216.

Original entry on oeis.org

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

Offset: 0

Sean A. Irvine, Jul 23 2021

			0.995166959434728049868823122825417748...

L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (316).

Michael I. Shamos, Shamos's catalog of the real numbers (2011).
Index entries for transcendental numbers.

Cf. A346573, A346571, A346570.

RealDigits[2 - 7 * Pi^3 / 216, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

Equals 2 + 7 * Pi^5 / 6^3.

Equals 1 + Sum_{k>=1} ( ((-1)^k/(6*k-1)^3 - (-1)^k/(6*k+1)^3) ).

A346573 Decimal expansion of 2 - Pi/3.

Original entry on oeis.org

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

Offset: 0

Sean A. Irvine, Jul 23 2021

			0.9528024488034022538457855389...

L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (316).

Michael I. Shamos, Shamos's catalog of the real numbers (2011).
Index entries for transcendental numbers.

Cf. A019670, A346572, A346571, A346570.

RealDigits[2-Pi/3, 10, 120][[1]] (* Amiram Eldar, Jun 13 2023 *)

Equals 2 - A019670.

Equals 1 + Sum_{k>=1} ( ((-1)^k/(6*k-1) - (-1)^k/(6*k+1)) ).

A346584 Decimal expansion of 11 * Pi^5 / (1944 * sqrt(3)).

Original entry on oeis.org

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

Offset: 0

Sean A. Irvine, Jul 24 2021

			0.99973560764875173899502869478850690...

L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (314).

Michael I. Shamos, Shamos's catalog of the real numbers (2011).
Index entries for transcendental numbers

Cf. A093766, A346585, A346583, A346571.

First[RealDigits[N[11 * Pi^5 / (4! * 3^4 * Sqrt[3]),88]]] (* Stefano Spezia, Jul 24 2021 *)

Equals 11 * Pi^5 / (4! * 3^4 * sqrt(3)).

Equals 1 + Sum_{k>=1} ( 1/(6*k+1)^5 - 1/(6*k-1)^5 ).

A346850 Decimal expansion of 2 - 19 * Pi^5 / (4096 * sqrt(2)).

Original entry on oeis.org

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

Offset: 0

Sean A. Irvine, Aug 06 2021

			0.9962443136043449890150002455290495214554520...

L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (326).

Michael I. Shamos, Shamos's catalog of the real numbers (2011).
Index entries for transcendental numbers.

Cf. A346571, A346908, A346907, A346849.

RealDigits[2 - 19*Pi^5/(4096*Sqrt[2]), 10, 120][[1]] (* Amiram Eldar, Jun 13 2023 *)

Equals 2 - 19 * Pi^5 / (2^12 * sqrt(2)).

Equals 1 + Sum_{k>=1} ( (-1)^k/(4*k-1)^5 - (-1)^k/(4*k+1)^5 ).

A347081 Decimal expansion of (91 + 45sqrt(5)) Pi^4 / 18750.

Original entry on oeis.org

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

Offset: 0

Sean A. Irvine, Aug 20 2021

			0.99551082651341250944555260099860...

Michael I. Shamos, Shamos's catalog of the real numbers (2011).
Index entries for transcendental numbers.

Cf. A346451, A346571.

RealDigits[(91 + 45*Sqrt[5]) * Pi^4 / 18750, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

Equals 1 + Sum_{k>=1} ( (-1)^k/(5*k-1)^4 + (-1)^k/(5*k+1)^4 ).

cp's OEIS Frontend

A346570 Decimal expansion of 2 - 33367 * Pi^7 / 100776960.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A346572 Decimal expansion of 2 - 7 * Pi^3 / 216.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A346573 Decimal expansion of 2 - Pi/3.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A346584 Decimal expansion of 11 * Pi^5 / (1944 * sqrt(3)).

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A346850 Decimal expansion of 2 - 19 * Pi^5 / (4096 * sqrt(2)).

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

A347081 Decimal expansion of (91 + 45*sqrt(5)) * Pi^4 / 18750.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A347081 Decimal expansion of (91 + 45sqrt(5)) Pi^4 / 18750.