@@ Property / constraint @@
+ ${\displaystyle{\displaystyle n=0,1,2,\dots}}$ 
n=0,1,2,\dots
@@ Property / constraint: ${\displaystyle{\displaystyle n=0,1,2,\dots}}$ / rank @@
+Normal rank
@@ Property / Symbols used @@
+Q10920
@@ Property / Symbols used: Q10920 / rank @@
+Normal rank
@@ Property / Symbols used: Q10920 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$ 
\LegendrepolyP{\NVar{n}}@{\NVar{x}}
@@ Property / Symbols used: Q10920 / qualifier @@
+xml-id: C18.S3.T1.t1.r10.m2acdec
@@ Property / Symbols used @@
+principal branch of logarithm function
@@ Property / Symbols used: principal branch of logarithm function / rank @@
+Normal rank
@@ Property / Symbols used: principal branch of logarithm function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\ln\NVar{z}}}$ 
\ln@@{\NVar{z}}
@@ Property / Symbols used: principal branch of logarithm function / qualifier @@
+xml-id: C4.S2.E2.m2aadec
@@ Property / Symbols used @@
+Q11448
@@ Property / Symbols used: Q11448 / rank @@
+Normal rank
@@ Property / Symbols used: Q11448 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}$ 
\assLegendreQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreQ[0]{\nu}@{z}
@@ Property / Symbols used: Q11448 / qualifier @@
+xml-id: C14.S2.SS2.p2.m5aadec
@@ 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.m1fdec
@@ Property / Symbols used @@
+Q11602
@@ Property / Symbols used: Q11602 / rank @@
+Normal rank
@@ Property / Symbols used: Q11602 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle n}}$ 
n
@@ Property / Symbols used: Q11602 / qualifier @@
+xml-id: C14.S1.XMD6.m1edec
@@ Property / Symbols used @@
+Q11603
@@ Property / Symbols used: Q11603 / rank @@
+Normal rank
@@ Property / Symbols used: Q11603 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle W_{n-1}(x)}}$ 
W_{n-1}(x)
@@ Property / Symbols used: Q11603 / qualifier @@
+xml-id: C14.S7.XMD1.m1ddec

DLMF:14.7.E7 (Q4759): Difference between revisions

n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}

P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}

x 𝑥 {\displaystyle{\displaystyle x}}

n 𝑛 {\displaystyle{\displaystyle n}}

W n - 1 ⁢ ( x ) subscript 𝑊 𝑛 1 𝑥 {\displaystyle{\displaystyle W_{n-1}(x)}}

Latest revision as of 01:28, 2 January 2020

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${\displaystyle{\displaystyle n=0,1,2,\dots}}$

${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$

${\displaystyle{\displaystyle\ln\NVar{z}}}$

${\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}$

${\displaystyle{\displaystyle x}}$

${\displaystyle{\displaystyle n}}$

${\displaystyle{\displaystyle W_{n-1}(x)}}$