A247671 - OEIS

A247671

Decimal expansion of Sum_{n >= 1} coth(Pi*n)/n^7 = (19/56700)*Pi^7.

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

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OFFSET

1,4

COMMENTS

This identity was discovered by Ramanujan.

REFERENCES

G. H. Hardy, P. V. Seshu Aiyar, and B. M. Wilson, Collected Papers of Srinivasa Ramanujan, Chelsea Publishing Co., N.Y., 1962. See p. xxvi, eq. (5).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Philippe Flajolet and Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998), p. 34.

H. F. Sandham, Three summations due to Ramanujan, The Quarterly Journal of Mathematics, Vol. 1, No. 1 (1950), pp. 238-240.

H. F. Sandham, Some infinite series, Proc. Amer. Math. Soc., Vol. 5 (1954), pp. 430-436. See p. 431, eq. 1.42.

Index entries for transcendental numbers.

FORMULA

Sum_{n >= 1} coth(Pi*n)/n^7 = (19/56700)*Pi^7.

EXAMPLE

1.012091205075115507632626514433312077714836279199517513...

MATHEMATICA

RealDigits[(19/56700)*Pi^7, 10, 100] // First

PROG

(PARI) default(realprecision, 100); (19/56700)*Pi^7 \\ G. C. Greubel, Aug 31 2018

(Magma) R:= RealField(100); (19/56700)*Pi(R)^7; // G. C. Greubel, Aug 31 2018

CROSSREFS

Cf. A084258.

Sequence in context: A362952 A237289 A238396 * A011125 A345364 A197583

Adjacent sequences: A247668 A247669 A247670 * A247672 A247673 A247674

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Sep 22 2014

STATUS

approved