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 A277235 Decimal expansion of 2/(Gamma(3/4))^4. 3
 8, 8, 6, 9, 4, 1, 1, 6, 8, 5, 7, 8, 1, 1, 5, 4, 0, 5, 4, 1, 1, 5, 2, 5, 3, 6, 1, 3, 5, 4, 5, 2, 1, 5, 3, 8, 6, 8, 6, 4, 9, 9, 9, 1, 9, 6, 4, 2, 5, 9, 8, 3, 4, 8, 3, 0, 9, 8, 6, 0, 9, 8, 9, 8, 1, 3, 1, 7, 8, 2, 5, 5, 9, 4, 8, 1, 9, 2, 7, 9, 7, 0, 6, 9, 1, 5, 2, 6, 4, 7, 7, 9, 4, 9, 8, 1, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the value of one of Ramanujan's series: 1 - 5*(1/2)^5 + 9*(1*3/(2*4))^5 -13*(1*3*5/(2*4*6))^5 + - ... . See the Hardy reference p.7. eq. (1.4) and pp. 105-106. For the partial sums see A278140. The proof of Hardy and Whipple mentioned in the Hardy reference reduces this series to (2/Pi)*Morley's series (for m=1/2). For this series see A277232 and A091670. REFERENCES G. H. Hardy, Ramanujan, AMS Chelsea Publ., Providence, RI, 2002, pp. 7, 105-106, 111. LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 FORMULA Equals Sum_{k=0..n} (1+4*k)*(binomial(-1/2,k))^5 = Sum_{k=0..n} (-1)^k*(1+4*k)*((2*k-1)!!/(2*k)!!)^5. The double factorials are given in A001147 and A000165 with (-1)!! := 1. Equals A060294 * A091670. For (1+4*k)*((2*k-1)!!/(2*k)!!)^5 see A074799(k) / A074800(k). EXAMPLE 2/Gamma(3/4)^4 = 0.88694116857811540541152... MATHEMATICA RealDigits[2/(Gamma[3/4])^4, 10, 100][[1]] (* G. C. Greubel, Oct 26 2018 *) PROG (PARI) 2/gamma(3/4)^4 \\ Michel Marcus, Nov 13 2016 (MAGMA) SetDefaultRealField(RealField(100)); 2/(Gamma(3/4))^4; // G. C. Greubel, Oct 26 2018 CROSSREFS Cf. A060294, A074799, A074800, A091670, A277232, A278140. Sequence in context: A140976 A253270 A021057 * A241058 A248570 A242051 Adjacent sequences:  A277232 A277233 A277234 * A277236 A277237 A277238 KEYWORD nonn,cons AUTHOR Wolfdieter Lang, Nov 13 2016 STATUS approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)