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: 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)) .