@@ Property / constraint @@
+ ${\displaystyle{\displaystyle\Re(\nu+1)>\Re\mu>-\tfrac{1}{2}}}$ 
\realpart@@{(\nu+1)}>\realpart@@{\mu}>-\tfrac{1}{2}
+Normal rank
@@ Property / Symbols used @@
+gamma function
@@ Property / Symbols used: gamma function / rank @@
+Normal rank
@@ Property / Symbols used: gamma function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ 
\EulerGamma@{\NVar{z}}
@@ Property / Symbols used: gamma function / qualifier @@
+xml-id: C5.S2.E1.m2aadec
@@ Property / Symbols used @@
+Q11592
@@ Property / Symbols used: Q11592 / rank @@
+Normal rank
@@ Property / Symbols used: Q11592 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}$ 
\assLegendreOlverQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: Q11592 / qualifier @@
+xml-id: C14.S21.SS1.p1.m3adec
@@ Property / Symbols used @@
+the ratio of the circumference of a circle to its diameter
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle\pi}}$ 
\cpi
+xml-id: C3.S12.E1.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 @@
+hyperbolic cosine function
@@ Property / Symbols used: hyperbolic cosine function / rank @@
+Normal rank
@@ Property / Symbols used: hyperbolic cosine function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\cosh\NVar{z}}}$ 
\cosh@@{\NVar{z}}
@@ Property / Symbols used: hyperbolic cosine function / qualifier @@
+xml-id: C4.S28.E2.m2aadec
@@ 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.m2aadec
@@ 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 @@
+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 @@
+Q11638
@@ Property / Symbols used: Q11638 / rank @@
+Normal rank
@@ Property / Symbols used: Q11638 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q11638 / qualifier @@
+xml-id: C14.S1.XMD4.m1adec
@@ Property / Symbols used @@
+Q11591
@@ Property / Symbols used: Q11591 / rank @@
+Normal rank
@@ Property / Symbols used: Q11591 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mu}}$ 
\mu
@@ Property / Symbols used: Q11591 / qualifier @@
+xml-id: C14.S1.XMD7.m1adec
@@ Property / Symbols used @@
+Q11590
@@ Property / Symbols used: Q11590 / rank @@
+Normal rank
@@ Property / Symbols used: Q11590 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\nu}}$ 
\nu
@@ Property / Symbols used: Q11590 / qualifier @@
+xml-id: C14.S1.XMD8.m1adec

DLMF:14.25.E2 (Q4959): Difference between revisions

ℜ ⁡ ( ν + 1 ) > ℜ ⁡ μ > - 1 2 𝜈 1 𝜇 1 2 {\displaystyle{\displaystyle\Re(\nu+1)>\Re\mu>-\tfrac{1}{2}}}

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}

π {\displaystyle{\displaystyle\pi}}

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

cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

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

∫ {\displaystyle{\displaystyle\int}}

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

z 𝑧 {\displaystyle{\displaystyle z}}

μ 𝜇 {\displaystyle{\displaystyle\mu}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

Latest revision as of 13:42, 2 January 2020

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

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

${\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}$

${\displaystyle{\displaystyle\pi}}$

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

${\displaystyle{\displaystyle\cosh\NVar{z}}}$

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

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

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

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle\mu}}$

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