Incomplete gamma function
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In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals.
The upper incomplete gamma function for some values of s: 0 (blue), 1 (red), 2 (green), 3 (orange), 4 (purple).
Euler's constant
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Euler's constant is a mathematical constant, usually denoted by the lowercase Greek letter gamma, defined as the limiting difference between the harmonic series and the natural logarithm, denoted here
Incomplete gamma function
…1 ∞ ( − z ) k k ! ( s + k ) , ℜ ( s ) > − 1 , s ≠ 0. When s → 0: z s − 1 s → ln ( z ) , Γ ( s ) − 1 s = 1 s − γ + O ( s ) − 1 s → − γ , ( γ is the Euler–Mascheroni constant here), hence, Γ ( 0 , z ) = lim s → 0 ( Γ ( s ) − 1 s − ( γ ( s , z ) − 1 s ) ) = − γ − ln ( z ) − ∑ k = 1 ∞ ( − z ) k k ( k ! ) is the limiting…
Generalisation of Euler–Mascheroni constant