@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\Re(s_{j})>\frac{1}{2}(j-1)}}$ 
\Re(s_{j})>\frac{1}{2}(j-1)
+Normal rank
@@ Property / constraint @@
+ ${\displaystyle{\displaystyle j=1,\dots,m}}$ 
j=1,\dots,m
@@ Property / constraint: ${\displaystyle{\displaystyle j=1,\dots,m}}$ / rank @@
+Normal rank
@@ Property / Symbols used @@
+Q10923
@@ Property / Symbols used: Q10923 / rank @@
+Normal rank
@@ Property / Symbols used: Q10923 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathbb{C}}}$ 
\Complexes
@@ Property / Symbols used: Q10923 / qualifier @@
+xml-id: introduction.Sx4.p1.t1.r1.m2adec
@@ Property / Symbols used @@
+Q10770
@@ Property / Symbols used: Q10770 / rank @@
+Normal rank
@@ Property / Symbols used: Q10770 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ 
\diff{\NVar{x}}
@@ Property / Symbols used: Q10770 / qualifier @@
+xml-id: C1.S4.SS4.m1aadec
@@ Property / Symbols used @@
+Q10784
@@ Property / Symbols used: Q10784 / rank @@
+Normal rank
@@ Property / Symbols used: Q10784 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\in}}$ 
\in
@@ Property / Symbols used: Q10784 / qualifier @@
+xml-id: introduction.Sx4.p1.t1.r10.m2adec
@@ Property / Symbols used @@
+Q12718
@@ Property / Symbols used: Q12718 / rank @@
+Normal rank
@@ Property / Symbols used: Q12718 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}$ 
\exptrace@{\NVar{\mathbf{X}}}
@@ Property / Symbols used: Q12718 / qualifier @@
+xml-id: C35.S1.p3.t1.r10.m3aadec
@@ Property / Symbols used @@
+Q10771
@@ Property / Symbols used: Q10771 / rank @@
+Normal rank
@@ Property / Symbols used: Q10771 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\int}}$ 
\int
@@ Property / Symbols used: Q10771 / qualifier @@
+xml-id: C1.S4.SS4.m3aadec
@@ Property / Symbols used @@
+Q12725
@@ Property / Symbols used: Q12725 / rank @@
+Normal rank
@@ Property / Symbols used: Q12725 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}$ 
\multivarEulerGamma{\NVar{m}}@{\NVar{a}}
@@ Property / Symbols used: Q12725 / qualifier @@
+xml-id: C35.S3.SS1.m1aadec
@@ Property / Symbols used @@
+Q10811
@@ Property / Symbols used: Q10811 / rank @@
+Normal rank
@@ Property / Symbols used: Q10811 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Re}}$ 
\realpart@@
@@ Property / Symbols used: Q10811 / qualifier @@
+xml-id: C1.S9.E2.m1aadec
@@ Property / Symbols used @@
+Q12719
@@ Property / Symbols used: Q12719 / rank @@
+Normal rank
@@ Property / Symbols used: Q12719 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathbf{X}}}$ 
\mathbf{X}
@@ Property / Symbols used: Q12719 / qualifier @@
+xml-id: C35.S1.XMD12.m1adec
@@ Property / Symbols used @@
+Q12720
@@ Property / Symbols used: Q12720 / rank @@
+Normal rank
@@ Property / Symbols used: Q12720 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}$ 
{\boldsymbol{\Omega}}
@@ Property / Symbols used: Q12720 / qualifier @@
+xml-id: C35.S1.XMD13.m1adec
@@ Property / Symbols used @@
+Q12727
@@ Property / Symbols used: Q12727 / rank @@
+Normal rank
@@ Property / Symbols used: Q12727 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle j}}$ 
j
@@ Property / Symbols used: Q12727 / qualifier @@
+xml-id: C35.S1.XMD4.m1dec
@@ Property / Symbols used @@
+Q12723
@@ Property / Symbols used: Q12723 / rank @@
+Normal rank
@@ Property / Symbols used: Q12723 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle m}}$ 
m
@@ Property / Symbols used: Q12723 / qualifier @@
+xml-id: C35.S1.XMD8.m1adec

DLMF:35.3.E2 (Q9778): Difference between revisions

ℜ ⁡ ( s j ) > 1 2 ⁢ ( j - 1 ) subscript 𝑠 𝑗 1 2 𝑗 1 {\displaystyle{\displaystyle\Re(s_{j})>\frac{1}{2}(j-1)}}

j = 1 , … , m 𝑗 1 … 𝑚 {\displaystyle{\displaystyle j=1,\dots,m}}

ℂ {\displaystyle{\displaystyle\mathbb{C}}}

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

∈ {\displaystyle{\displaystyle\in}}

etr ⁡ ( 𝐗 ) exponential-trace 𝐗 {\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}

∫ {\displaystyle{\displaystyle\int}}

Γ m ⁡ ( a ) multivariate-Euler-Gamma 𝑚 𝑎 {\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

𝐗 𝐗 {\displaystyle{\displaystyle\mathbf{X}}}

𝛀 𝛀 {\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}

j 𝑗 {\displaystyle{\displaystyle j}}

m 𝑚 {\displaystyle{\displaystyle m}}

Latest revision as of 14:48, 2 January 2020

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${\displaystyle{\displaystyle\Re(s_{j})>\frac{1}{2}(j-1)}}$

${\displaystyle{\displaystyle j=1,\dots,m}}$

${\displaystyle{\displaystyle\mathbb{C}}}$

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

${\displaystyle{\displaystyle\in}}$

${\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}$

${\displaystyle{\displaystyle\int}}$

${\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}$

${\displaystyle{\displaystyle\Re}}$

${\displaystyle{\displaystyle\mathbf{X}}}$

${\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}$

${\displaystyle{\displaystyle j}}$

${\displaystyle{\displaystyle m}}$