예제 #1
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        }// end  int Moebius_Mi( Int64 theIsolatedNatural )

        /// <summary>
        /// It's an integral function (in the sense of a cumulative function).
        /// NB. have to start from (+1) not from zero !!!!
        /// </summary>
        /// <param name="theIsolatedNatural"></param>
        /// <returns></returns>
        public static long Mertens_M(Int64 theIsolatedNatural)
        {                                                 // It's an integral function (in the sense of a cumulative function).
            long Mertens_M = 0L;                          // sum on it; it's the reduct of a series.

            for (int c = 1; c <= theIsolatedNatural; c++) // NB. have to start from (+1) not from zero !!!!
            {                                             // NB. have to start from (+1) not from zero !!!!
                Mertens_M += ElementFullCalculation.Moebius_Mi(c);
            }// end for : // NB. have to start from (+1) not from zero !!!!
            // ready
            return(Mertens_M);
        }// end  long Mertens_M( Int64 theIsolatedNatural )
예제 #2
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        }// end int DiracDelta_Omegas( Int64 theIsolatedNatural )

        public static int Moebius_Mi(Int64 theIsolatedNatural)
        {
            if (+1L > theIsolatedNatural)
            {
                throw new System.Exception("Omega functions are defined for n in N, n>=+1.");
            }// else can continue.
            //
            int DiracDelta_onOmegas = ElementFullCalculation.DiracDelta_Omegas(theIsolatedNatural);
            int Lambda = ElementFullCalculation.Lambda_Liouville(theIsolatedNatural);

            // ready
            return(DiracDelta_onOmegas * Lambda);
        }// end  int Moebius_Mi( Int64 theIsolatedNatural )