DLMF:13.14.E18 (Q4507): Difference between revisions

Revision as of 16:06, 2 January 2020

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English	DLMF:13.14.E18	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(2% \mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}z^{\frac{1}{2}-\mu}+% \frac{\Gamma\left(-2\mu\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}z^{% \frac{1}{2}+\mu}+O\left(z^{\frac{3}{2}-\Re\mu}\right),}}

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DLMF id

DLMF:13.14.E18

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constraint

{\displaystyle{\displaystyle 0\leq\Re\mu<\tfrac{1}{2}}}

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{\displaystyle{\displaystyle 0\leq\Re\mu<\tfrac{1}{2}}}

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{\displaystyle{\displaystyle\mu\not=0}}

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Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2addec

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gamma function

Defining formula

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

xml-id

C5.S2.E1.m2afdec

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Whittaker confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

xml-id

C13.S14.E3.m2aidec

0 references

Q10811

Defining formula

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}

xml-id

C1.S9.E2.m1aadec

0 references

Q11557

Defining formula

{\displaystyle{\displaystyle z}}

xml-id

C13.S1.XMD6.m1qdec

0 references

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2addec

0 references

@@ 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.m2addec

DLMF:13.14.E18 (Q4507): Difference between revisions

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

Revision as of 16:06, 2 January 2020

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DLMF:13.14.E18 (Q4507): Difference between revisions

O â¡ ( \NVar â¢ x ) Big-O \NVar ð¥ {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

Revision as of 16:06, 2 January 2020

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