The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241420 Decimal expansion of D(1/2), where D(x) is the infinite product function defined in the formula section (or in the Finch reference). 3
 1, 5, 4, 9, 1, 2, 6, 5, 9, 2, 5, 7, 7, 5, 6, 2, 1, 6, 8, 3, 6, 9, 5, 7, 2, 5, 3, 3, 8, 4, 9, 4, 0, 9, 9, 2, 6, 9, 3, 7, 0, 2, 9, 8, 6, 3, 4, 1, 0, 0, 4, 8, 3, 6, 2, 8, 9, 9, 9, 9, 6, 7, 1, 0, 3, 9, 9, 8, 3, 8, 0, 0, 8, 3, 6, 5, 4, 3, 2, 9, 8, 7, 4, 0, 6, 5, 1, 1, 4, 0, 9, 2, 0, 7, 0, 0, 8, 0, 6, 1, 5, 4, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin Constant, p. 136. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 20. Eric Weisstein's MathWorld, Barnes G-Function Eric Weisstein's MathWorld, Catalan's Constant Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant FORMULA D(x) = lim_{n->infinity} ( prod_{k=1..2n+1} (1+x/k)^((-1)^(k+1)*k) ). D(x) = (e^(x/2-1/4)*A^3*G((x+1)/2)^2*Gamma(x/2)^(x-2)*Gamma((x+1)/2)^(1-x)*(Gamma((x+1)/2)/Gamma(x/2))^x)/(2^(1/12)*G(x/2)^2), where A is the Glaisher-Kinkelin constant and G is the Barnes G-function. D(1/2) = (e^(C/Pi)*A^3*sqrt(Gamma(3/4)/Gamma(1/4)))/2^(1/12), where C is Catalan's constant. EXAMPLE 1.54912659257756216836957253384940992693702986341004836289999671... MATHEMATICA (E^(Catalan/Pi)*Glaisher^3*Sqrt[Gamma[3/4]/Gamma[1/4]])/2^(1/12) // RealDigits[#, 10, 104]& // First PROG (PARI) default(realprecision, 100); A=exp(1/12-zeta'(-1)); exp(Catalan/Pi)*A^3*sqrt(gamma(3/4)/gamma(1/4))/2^(1/12) \\ G. C. Greubel, Aug 24 2018 CROSSREFS Cf. A006752, A019610 (D(2)), A074962, A241421 (D(1)). Sequence in context: A215337 A090124 A097943 * A077142 A156057 A125057 Adjacent sequences:  A241417 A241418 A241419 * A241421 A241422 A241423 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Aug 08 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 20 22:47 EST 2020. Contains 332086 sequences. (Running on oeis4.)