Exponential, Logarithmic, Sine, and Cosine Integrals - 6.15 Sums

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
6.15.E1	${\displaystyle{\displaystyle\sum_{n=1}^{\infty}\mathrm{Ci}\left(\pi n\right)=\tfrac{1}{2}(\ln 2-\gamma)}}$ \sum_{n=1}^{\infty}\cosint@{\pi n} = \tfrac{1}{2}(\ln@@{2}-\EulerConstant)		sum(Ci(Pi*n), n = 1..infinity) = (1)/(2)*(ln(2)- gamma)	Sum[CosIntegral[Pi*n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*(Log[2]- EulerGamma)	Failure	Failure	Successful [Tested: 0]	Failed [1 / 1] Result: Plus[-0.05796575782920621, NSum[CosIntegral[Times[n, Pi]] Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
6.15.E2	${\displaystyle{\displaystyle\sum_{n=1}^{\infty}\frac{\mathrm{si}\left(\pi n\right)}{n}=\tfrac{1}{2}\pi(\ln\pi-1)}}$ \sum_{n=1}^{\infty}\frac{\shiftsinint@{\pi n}}{n} = \tfrac{1}{2}\pi(\ln@@{\pi}-1)		sum((Ssi(Pi*n))/(n), n = 1..infinity) = (1)/(2)*Pi*(ln(Pi)- 1)	Sum[Divide[SinIntegral[Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Divide[1,2]*Pi*(Log[Pi]- 1)	Failure	Failure	Successful [Tested: 0]	Failed [1 / 1] Result: Plus[-0.22734117306968246, NSum[Times[Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[n, Pi]]]] Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
6.15.E3	${\displaystyle{\displaystyle\sum_{n=1}^{\infty}(-1)^{n}\mathrm{Ci}\left(2\pi n\right)=1-\ln 2-\tfrac{1}{2}\gamma}}$ \sum_{n=1}^{\infty}(-1)^{n}\cosint@{2\pi n} = 1-\ln@@{2}-\tfrac{1}{2}\EulerConstant		sum((- 1)^(n)* Ci(2*Pi*n), n = 1..infinity) = 1 - ln(2)-(1)/(2)*gamma	Sum[(- 1)^(n)* CosIntegral[2*Pi*n], {n, 1, Infinity}, GenerateConditions->None] == 1 - Log[2]-Divide[1,2]*EulerGamma	Failure	Failure	Successful [Tested: 0]	Failed [1 / 1] Result: Plus[-0.018244986989288337, NSum[Times[Power[-1, n], CosIntegral[Times[2, n, Pi]]] Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}
6.15.E4	${\displaystyle{\displaystyle\sum_{n=1}^{\infty}(-1)^{n}\frac{\mathrm{si}\left(2\pi n\right)}{n}=\pi(\tfrac{3}{2}\ln 2-1)}}$ \sum_{n=1}^{\infty}(-1)^{n}\frac{\shiftsinint@{2\pi n}}{n} = \pi(\tfrac{3}{2}\ln@@{2}-1)		sum((- 1)^(n)*(Ssi(2*Pi*n))/(n), n = 1..infinity) = Pi*((3)/(2)*ln(2)- 1)	Sum[(- 1)^(n)*Divide[SinIntegral[2*Pi*n] - Pi/2,n], {n, 1, Infinity}, GenerateConditions->None] == Pi*(Divide[3,2]*Log[2]- 1)	Failure	Failure	Successful [Tested: 0]	Failed [1 / 1] Result: Plus[-0.12478648186560967, NSum[Times[Power[-1, n], Power[n, -1], Plus[Times[Rational[-1, 2], Pi], SinIntegral[Times[2, n, Pi]]]] Test Values: {n, 1, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {}