

A337981


Decimal expansion of Pi*BesselY(0,2)/(2*BesselJ(0,2))  gamma, where BesselJ and BesselY are the Bessel functions of the first and second kind, respectively, and gamma is Euler's constant (A001620).


0



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

1,1


COMMENTS

This constant is transcendental (Mahler, 1968).
Mahler's proof was obtained as a result of his attempt to prove that Euler's constant gamma (A001620) is transcendental. For one week he believed that he had succeeded in proving the transcendence of both gamma and exp(gamma) (Mahler, 1982).


REFERENCES

Kurt Mahler, Lectures on Transcendental Numbers, SpringerVerlag, 1976. See. p. 184.
David Masser, Auxiliary Polynomials in Number Theory, Cambridge University Press, 2016. See p. 307.


LINKS



FORMULA

Equals Sum_{k>=1} (1)^(k+1) * H(k)/(k!)^2 / Sum_{k>=0} (1)^k/(k!)^2, where H(k) = A001008(k)/A002805(k) is the kth harmonic number.


EXAMPLE

3.00353131788494903906815068081107618814007054517065...


MATHEMATICA

RealDigits[Pi*BesselY[0, 2]/BesselJ[0, 2]/2  EulerGamma, 10, 100][[1]]


PROG



CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



