DLMF:10.20.E6 (Q3255): Difference between revisions

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Revision as of 15:38, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:38, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Q11426
		Property / Symbols used: Q11426 / rank
			Normal rank
		Property / Symbols used: Q11426 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11426 / qualifier
			xml-id: C10.S1.XMD6.m1edec
		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.m1bdec
		Property / Symbols used
			Q11451
		Property / Symbols used: Q11451 / rank
			Normal rank
		Property / Symbols used: Q11451 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta(z)}}$ \zeta(z)
		Property / Symbols used: Q11451 / qualifier
			xml-id: C10.S20.XMD1.m1edec
		Property / Symbols used
			coefficients (locally)
		Property / Symbols used: coefficients (locally) / rank
			Normal rank
		Property / Symbols used: coefficients (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle A_{k}(\zeta)}}$ A_{k}(\zeta)
		Property / Symbols used: coefficients (locally) / qualifier
			xml-id: C10.S20.XMD4.m1bdec
		Property / Symbols used
			coefficients (locally)
		Property / Symbols used: coefficients (locally) / rank
			Normal rank
		Property / Symbols used: coefficients (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle B_{k}(\zeta)}}$ B_{k}(\zeta)
		Property / Symbols used: coefficients (locally) / qualifier
			xml-id: C10.S20.XMD5.m1bdec

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Latest revision as of 15:38, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.20.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\rselection{{H^{(1)}_{\nu}}\left(\nu z\right)\\ {H^{(2)}_{\nu}}\left(\nu z\right)}\sim 2e^{\mp\pi i/3}\left(\frac{4\zeta}{1-z^{2}}\right)^{\frac{1}{4}}\left(\frac{\mathrm{Ai}\left(e^{\pm 2\pi i/3}\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{1}{3}}}\sum_{k=0}^{\infty}\frac{A_{k}(\zeta)}{\nu^{2k}}+\frac{e^{\pm 2\pi i/3}\mathrm{Ai}'\left(e^{\pm 2\pi i/3}\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{5}{3}}}\sum_{k=0}^{\infty}\frac{B_{k}(\zeta)}{\nu^{2k}}\right),}}$

0 references

DLMF id

DLMF:10.20.E6

0 references

Symbols used

Q10919

Defining formula

${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$

xml-id

C9.S2.SS1.m1aadec

0 references

Bessel function of the third kind (or Hankel function)

Defining formula

${\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E5.m2adec

0 references

Bessel function of the third kind (or Hankel function)

Defining formula

${\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E6.m2adec

0 references

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2adec

0 references

Q11428

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C10.S1.XMD3.m1bdec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1edec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1bdec

0 references

Q11451

Defining formula

${\displaystyle{\displaystyle\zeta(z)}}$

xml-id

C10.S20.XMD1.m1edec

0 references

coefficients (locally)

Defining formula

${\displaystyle{\displaystyle A_{k}(\zeta)}}$

xml-id

C10.S20.XMD4.m1bdec

0 references

coefficients (locally)

Defining formula

${\displaystyle{\displaystyle B_{k}(\zeta)}}$

xml-id

C10.S20.XMD5.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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