Compute series and integrals involving the Euler-Mascheroni constant gamma ≈ 0.5772. Applications: harmonic number approximation H_n ≈ ln(n)+gamma, digamma function psi(1)=-gamma, and regularization of divergent series.
| Constant | Symbol | Value |
|---|---|---|
| Speed of light | c | 2.99792458×10⁸ |
| Planck's constant | h | 6.62607015×10⁻³‴ |
| Boltzmann constant | kʙ | 1.380649×10⁻²³ |
| Avogadro's number | Nₐ | 6.02214076×10²³ |
| Gravitational constant | G | 6.6743×10⁻¹¹ |
| Gas constant | R | 8.31446 |
| Elementary charge | e | 1.602176634×10⁻¹⁹ |
| Electron mass | mₑ | 9.1093837015×10⁻³¹ |
| Proton mass | mₚ | 1.67262192369×10⁻²⁷ |
| Fine-structure constant | α | 7.2973525693×10⁻³ |
Enter the values for the scenario you are assessing. Compute series and integrals involving the Euler-Mascheroni constant gamma ≈ 0.5772. Applications: harmonic number approximation H_n ≈ ln(n)+gamma, digamma function psi(1)=-gamma, and regularization of divergent series. Use the euler-mascheroni constant result to inform your calculation.