@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\Re(\mu\mp\nu)>-\tfrac{1}{2}}}$ 
\Re(\mu\mp\nu)>-\tfrac{1}{2}
+Normal rank
@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\Re(\mu\pm\nu)>-1}}$ 
\Re(\mu\pm\nu)>-1
@@ Property / constraint: ${\displaystyle{\displaystyle\Re(\mu\pm\nu)>-1}}$ / rank @@
+Normal rank
@@ Property / constraint @@
+ ${\displaystyle{\displaystyle x>0}}$ 
x>0
@@ Property / constraint: ${\displaystyle{\displaystyle x>0}}$ / rank @@
+Normal rank
@@ Property / Symbols used @@
+Bessel function of the first kind
@@ Property / Symbols used: Bessel function of the first kind / rank @@
+Normal rank
@@ Property / Symbols used: Bessel function of the first kind / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\BesselJ{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: Bessel function of the first kind / qualifier @@
+xml-id: C10.S2.E2.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.m1aodec
@@ Property / Symbols used @@
+base of natural logarithm
@@ Property / Symbols used: base of natural logarithm / rank @@
+Normal rank
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{e}}}$ 
\expe
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+xml-id: C4.S2.E11.m2aidec
@@ Property / Symbols used @@
+hyperbolic sine function
@@ Property / Symbols used: hyperbolic sine function / rank @@
+Normal rank
@@ Property / Symbols used: hyperbolic sine function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\sinh\NVar{z}}}$ 
\sinh@@{\NVar{z}}
@@ Property / Symbols used: hyperbolic sine function / qualifier @@
+xml-id: C4.S28.E1.m2acdec
@@ 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.m3aodec
@@ Property / Symbols used @@
+modified Bessel function of the first kind
@@ Property / Symbols used: modified Bessel function of the first kind / rank @@
+Normal rank
@@ Property / Symbols used: modified Bessel function of the first kind / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\modBesselI{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: modified Bessel function of the first kind / qualifier @@
+xml-id: C10.S25.E2.m2afdec
@@ Property / Symbols used @@
+modified Bessel function of the second kind
@@ Property / Symbols used: modified Bessel function of the second kind / rank @@
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\modBesselK{\NVar{\nu}}@{\NVar{z}}
+xml-id: C10.S25.E3.m2aidec
@@ 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.m1afdec
@@ Property / Symbols used @@
+Q11435
@@ Property / Symbols used: Q11435 / rank @@
+Normal rank
@@ Property / Symbols used: Q11435 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle x}}$ 
x
@@ Property / Symbols used: Q11435 / qualifier @@
+xml-id: C10.S1.XMD4.m1cdec
@@ Property / Symbols used @@
+Q11427
@@ Property / Symbols used: Q11427 / rank @@
+Normal rank
@@ Property / Symbols used: Q11427 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\nu}}$ 
\nu
@@ Property / Symbols used: Q11427 / qualifier @@
+xml-id: C10.S1.XMD7.m1kdec

DLMF:10.32.E16 (Q3536): Difference between revisions

ℜ ⁡ ( μ ∓ ν ) > - 1 2 minus-or-plus 𝜇 𝜈 1 2 {\displaystyle{\displaystyle\Re(\mu\mp\nu)>-\tfrac{1}{2}}}

ℜ ⁡ ( μ ± ν ) > - 1 plus-or-minus 𝜇 𝜈 1 {\displaystyle{\displaystyle\Re(\mu\pm\nu)>-1}}

x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}

J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

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

e {\displaystyle{\displaystyle\mathrm{e}}}

sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}

∫ {\displaystyle{\displaystyle\int}}

I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}

K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

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

x 𝑥 {\displaystyle{\displaystyle x}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

Latest revision as of 13:45, 2 January 2020

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${\displaystyle{\displaystyle\Re(\mu\mp\nu)>-\tfrac{1}{2}}}$

${\displaystyle{\displaystyle\Re(\mu\pm\nu)>-1}}$

${\displaystyle{\displaystyle x>0}}$

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

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

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle\sinh\NVar{z}}}$

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

${\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}$

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

${\displaystyle{\displaystyle x}}$

${\displaystyle{\displaystyle\nu}}$