Matching Tag: mittag-leffler-functions
Let 0 < α ≤ 1 2 0<\alpha\leq\frac{1}{2} 0 < α ≤ 2 1 E ρ , β E_{\rho,\beta} E ρ , β ρ \rho ρ β \beta β
Let c a l p h a a ∈ ( 3 5 , 1 ) calpha a\in\left(\frac{3}{5}, 1\right) c a l p haa ∈ ( 5 3 , 1 ) E α , 1 ( z ) E_{\alpha,1}(z) E α , 1 ( z )
The parameter-boundary conjecture. There exists an increasing convex function f : [ 2 , ∞ ) → [ 3 , ∞ ) f:[2,\infty)\to[3,\infty) f : [ 2 , ∞ ) → [ 3 , ∞ ) f ( 2 ) = 3 f(2)=3 f ( 2 ) = 3 α ≥ 2 \alpha\ge2 α ≥ 2
Smallest-zero conjecture for E α , 1 E_{\alpha,1} E α , 1 α ∈ ( 1 , 2 ] \alpha\in(1,2] α ∈ ( 1 , 2 ] E α , 1 ( − z α ) > 0 E_{\alpha,1}(-z^\alpha)>0 E α , 1 ( − z α ) > 0 z ∈ [ 0 , 1.559 ] z\in[0,1.559] z ∈ [ 0 , 1.559 ] α → 1 + \alpha\to1+ α → 1 +
Smallest-zero conjecture for E α , 2 E_{\alpha,2} E α , 2 α ∈ [ α 0 , 2 ] \alpha\in[\alpha_0,2] α ∈ [ α 0 , 2 ]
Smallest-zero conjecture for E α , α E_{\alpha,\alpha} E α , α α ∈ ( 1 , 2 ] \alpha\in(1,2] α ∈ ( 1 , 2 ] E α , α ( − z α ) > 0 E_{\alpha,\alpha}(-z^\alpha)>0 E α , α ( − z α ) > 0 z ∈ [ 0 , 2.93785 ] z\in[0,2.93785] z ∈ [ 0 , 2.93785 ] α → 1 + \alpha\to1+ α → 1 +
For α , β , γ > 0 \alpha,\beta,\gamma>0 α , β , γ > 0 F α , β ( γ ) F_{\alpha,\beta}^{(\gamma)} F α , β ( γ ) x > 0 x>0 x > 0
Let α ∈ ( 0 , 1 ] \alpha\in(0,1] α ∈ ( 0 , 1 ] m > 0 m>0 m > 0 l > m − 1 / α l>m-1/\alpha l > m − 1/ α x ≥ 0 x\geq 0 x ≥ 0 E α , m , l E_{\alpha,m,l} E α , m , l
Let α ∈ ( 0 , 1 ] \alpha\in(0,1] α ∈ ( 0 , 1 ] m > 0 m>0 m > 0 x ≥ 0 x\geq 0 x ≥ 0 E α , m , l E_{\alpha,m,l} E α , m , l G G G
