OFFSET
0,1
COMMENTS
In the Koecher reference v_5(3) = (2/5)*(present value V(5,3)) = 0.192680709798338..., given there as (1/4)*log(5) - (1/(2*sqrt(5)))*log((1 + sqrt(5))/2) - (Pi/10)*sqrt((5 - 2*sqrt(5))/5).
REFERENCES
Max Koecher, Klassische elementare Analysis, Birkhäuser, Basel, Boston, 1987, Eulersche Reihen, pp. 189 - 193.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Digamma Function
FORMULA
EXAMPLE
0.481701774495828777077075929361914755234187459374841804730459014188150...
MATHEMATICA
RealDigits[((5/2)*Log[5] - (2*GoldenRatio - 1)*(Log[GoldenRatio] + (Pi/5)*Sqrt[7 - 4*GoldenRatio]))/4, 10, 100][[1]] (* G. C. Greubel, Aug 30 2018 *)
PROG
(PARI) default(realprecision, 100); phi=(1+sqrt(5))/2; ((5/2)*log(5) - (2*phi-1)*(log(phi) + (Pi/5)*sqrt(7-4*phi)))/4 \\ G. C. Greubel, Aug 30 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); phi:= (1 + Sqrt(5))/2; ((5/2)*Log(5) - (2*phi-1)*(Log(phi) + (Pi(R)/5)*Sqrt(7 - 4*phi)))/4; // G. C. Greubel, Aug 30 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Wolfdieter Lang, Nov 16 2017
STATUS
approved