: ExpIntegralEi[1] - EulerGamma .

Many numbers associated with Zeta and Gamma can readily be generated, though apparently for example  and EulerGamma cannot. … If f[n] is a rational function, Sum[f[n], {n, ∞ }] must just be a linear combination of PolyGamma functions, but again the multivariate case can be much more complicated.

It is also known for example that Gamma[1/3] and BesselJ[0, n] are transcendental. It is not known for example whether EulerGamma is even irrational.

For large n this number is on average of order Log[n] + 2 EulerGamma - 1 . … For large n , DivisorSigma[1, n] is known to grow at most like Log[Log[n]] n Exp[EulerGamma] , and on average like π 2 /6 n (see page 1093 ).

Intrinsically defined curves With curvature given by a function f[s] of the arc length s , explicit coordinates {x[s], y[s]} of points are obtained from (compare page 1048 ) NDSolve[{x'[s]  Cos[ θ [s]], y'[s]  Sin[ θ [s]], θ '[s]  f[s], x[0]  y[0]  θ [0]  0}, {x, y, θ }, {s, 0, s max }] For various choices of f[s] , formulas for {x[s], y[s]} can be found using DSolve : f[s] = 1: {Sin[ θ ], Cos[ θ ]} f[s] = s: {FresnelS[ θ ], FresnelC[ θ ]} f[s] = 1/ √ s : √ θ {Sin[ √ θ ], Cos[ √ θ ]} f[s] = 1/s: θ {Cos[Log[ θ ]], Sin[Log[ θ ]]} f[s] = 1/s 2 : θ {Sin[1/ θ ], Cos[1/ θ ]} f[s] = s n : result involves Gamma[1/n, ±  θ n/n ] f[s] = Sin[s] : result involves Integrate[Sin[Sin[ θ ]], θ ] , expressible in terms of generalized Kampé de Fériet hypergeometric functions of two variables. … The general idea of so-called natural equations for obtaining curves from local curvature appears to have been first considered by Leonhard Euler in 1736.

For a cylinder, there are difficulties with boundary conditions at infinity, but the drag coefficient was nevertheless calculated by William Oseen in 1915 to be 8 π /(R (1/2 + Log[8/R] - EulerGamma)) .