メリン変換
ζ ( s ) = 1 Γ ( s ) ∫ 0 ∞ x s − 1 e x − 1 d x {\displaystyle \zeta (s)={\frac {1}{\Gamma (s)}}\int _{0}^{\infty }{\frac {x^{s-1}}{e^{x}-1}}dx}
↑ Hardy, G. H.; Littlewood, J. E. (1916). “Contributions to the Theory of the Riemann Zeta-Function and the Theory of the Distribution of Primes”. Acta Mathematica 41 (1): 119–196. doi:10.1007/BF02422942. (See notes therein for further references to Cahen's and Mellin's work, including Cahen's thesis.)
↑ Galambos & Simonelli (2004, p. 15)
1 2 3 Galambos & Simonelli (2004, p. 16)
↑ Galambos & Simonelli (2004, p. 23)