@@ Property / Symbols used @@
+order not exceeding
@@ Property / Symbols used: order not exceeding / rank @@
+Normal rank
@@ Property / Symbols used: order not exceeding / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$ 
\bigO@{\NVar{x}}
@@ Property / Symbols used: order not exceeding / qualifier @@
+xml-id: C2.S1.E3.m2aldec
@@ Property / Symbols used @@
+Q11481
@@ Property / Symbols used: Q11481 / rank @@
+Normal rank
@@ Property / Symbols used: Q11481 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$ 
\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
@@ Property / Symbols used: Q11481 / qualifier @@
+xml-id: C14.S21.SS1.p1.m1acdec
@@ 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.m2acdec
@@ Property / Symbols used @@
+Q11589
@@ Property / Symbols used: Q11589 / rank @@
+Normal rank
@@ Property / Symbols used: Q11589 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle x}}$ 
x
@@ Property / Symbols used: Q11589 / qualifier @@
+xml-id: C14.S1.XMD1.m1jdec
@@ 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.m1mdec
@@ 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.m1mdec
@@ Property / Symbols used @@
+Q11617
@@ Property / Symbols used: Q11617 / rank @@
+Normal rank
@@ Property / Symbols used: Q11617 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\beta}}$ 
\beta
@@ Property / Symbols used: Q11617 / qualifier @@
+xml-id: C14.S15.XMD10.m1bdec
@@ Property / Symbols used @@
+Q11618
@@ Property / Symbols used: Q11618 / rank @@
+Normal rank
@@ Property / Symbols used: Q11618 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle y}}$ 
y
@@ Property / Symbols used: Q11618 / qualifier @@
+xml-id: C14.S15.XMD11.m1bdec
@@ Property / Symbols used @@
+Q11619
@@ Property / Symbols used: Q11619 / rank @@
+Normal rank
@@ Property / Symbols used: Q11619 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\alpha}}$ 
\alpha
@@ Property / Symbols used: Q11619 / qualifier @@
+xml-id: C14.S15.XMD9.m1bdec

DLMF:14.15.E17 (Q4863): Difference between revisions

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

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

x 𝑥 {\displaystyle{\displaystyle x}}

μ 𝜇 {\displaystyle{\displaystyle\mu}}

ν 𝜈 {\displaystyle{\displaystyle\nu}}

β 𝛽 {\displaystyle{\displaystyle\beta}}

y 𝑦 {\displaystyle{\displaystyle y}}

α 𝛼 {\displaystyle{\displaystyle\alpha}}

Latest revision as of 01:51, 2 January 2020

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${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

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

${\displaystyle{\displaystyle x}}$

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

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

${\displaystyle{\displaystyle\beta}}$

${\displaystyle{\displaystyle y}}$

${\displaystyle{\displaystyle\alpha}}$