(21)=/e--d的解析性 关键也是证明它的一致收敛性 因为e--1=e+-1(x=Rez) a所以对于2平面上右半平面 的任一区域,有Rez≥0>0 t2-1≤ 而/-dt收敛 故(z,1)在z平面上右半平面内闭一致收敛 因此1(21)在右半平面解析
Gamma Function Beta Function Gamma Function: Definition Gamma Function: Analyticity Gamma Function: Properties γ(z, 1) = Z 1 0 e −t t z−1dt)Û5 ' ´y²§Âñ5 Ï e −t t z−1 = e−t t x−1 (x=Rez) ¤±éuz²¡þm²¡ ?«§kRe z ≥ δ > 0 e −t t z−1 ≤ t δ−1 Z 1 0 t δ−1 dtÂñ γ(z, 1)3z²¡þm²¡S4Âñ Ïdγ(z, 1)3m²¡)Û C. S. Wu 1nù Γ¼êB¼ê
(21)=/e--d的解析性 关键也是证明它的一致收敛性 因为e--1=e+-1(x=Rez) a所以对于2平面上右半平面 的任一区域,有Rez≥0>0 t2-1≤ 而/-dt收敛 故(z,1)在z平面上右半平面内闭一致收敛 因此(z,1)在右半平面解析
Gamma Function Beta Function Gamma Function: Definition Gamma Function: Analyticity Gamma Function: Properties γ(z, 1) = Z 1 0 e −t t z−1dt)Û5 ' ´y²§Âñ5 Ï e −t t z−1 = e−t t x−1 (x=Rez) ¤±éuz²¡þm²¡ ?«§kRe z ≥ δ > 0 e −t t z−1 ≤ t δ−1 Z 1 0 t δ−1 dtÂñ γ(z, 1)3z²¡þm²¡S4Âñ Ïdγ(z, 1)3m²¡)Û C. S. Wu 1nù Γ¼êB¼ê
(z)的解析性 e-tt2-ldt+/e-tt2-ldt 7(z,1) 「(z,1)
Gamma Function Beta Function Gamma Function: Definition Gamma Function: Analyticity Gamma Function: Properties Γ(z))Û5 Γ(z)=Z ∞ 0 e −t t z−1 dt= Z 1 0 e −t t z−1 dt | {z } γ(z, 1) + Z ∞ 1 e −t t z−1 dt | {z } Γ(z, 1) Γ(z, 1)3 ²¡)Û γ(z, 1)3m²¡)Û ÏdΓ(z)3m²¡)Û C. S. Wu 1nù Γ¼êB¼ê
(z)的解析性 e-tt2-ldt+/e-tt2-ldt 7(z,1) 「(z,1) °「(z,1)在全平面解析 (21)在右半平面解析 因此(2)在右半平面解
Gamma Function Beta Function Gamma Function: Definition Gamma Function: Analyticity Gamma Function: Properties Γ(z))Û5 Γ(z)=Z ∞ 0 e −t t z−1 dt= Z 1 0 e −t t z−1 dt | {z } γ(z, 1) + Z ∞ 1 e −t t z−1 dt | {z } Γ(z, 1) Γ(z, 1)3 ²¡)Û γ(z, 1)3m²¡)Û ÏdΓ(z)3m²¡)Û C. S. Wu 1nù Γ¼êB¼ê
(z)的解析性 e-tt2-ldt+/e-tt2-ldt 7(z,1) 「(z,1) 「(z,1)在全平面解析 °7(z,1)在右半平面解析 因此「(=)在右半平面解析
Gamma Function Beta Function Gamma Function: Definition Gamma Function: Analyticity Gamma Function: Properties Γ(z))Û5 Γ(z)=Z ∞ 0 e −t t z−1 dt= Z 1 0 e −t t z−1 dt | {z } γ(z, 1) + Z ∞ 1 e −t t z−1 dt | {z } Γ(z, 1) Γ(z, 1)3 ²¡)Û γ(z, 1)3m²¡)Û ÏdΓ(z)3m²¡)Û C. S. Wu 1nù Γ¼êB¼ê