DLMF:13.21.E3 (Q4611): Difference between revisions

From DRMF

Jump to navigation Jump to search

Revision as of 14:17, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 14:17, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
(2 intermediate revisions by the same user not shown)
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2adec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2adec
		Property / Symbols used
			Q11566
		Property / Symbols used: Q11566 / rank
			Normal rank
		Property / Symbols used: Q11566 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11566 / qualifier
			xml-id: C13.S1.XMD4.m1bdec

---

Latest revision as of 14:17, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.21.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{-\pi\mathrm{i}}\right)=\frac{\pi\sqrt{x}}{\Gamma\left(\kappa+\tfrac{1}{2}\right)}e^{\mu\pi\mathrm{i}}\*\left({H^{(1)}_{2\mu}}\left(2\sqrt{x\kappa}\right)+\mathrm{env}\mskip-2.0mu Y_{2\mu}\left(2\sqrt{x\kappa}\right)O\left(\kappa^{-\frac{1}{2}}\right)\right),}}$

0 references

DLMF id

DLMF:13.21.E3

0 references

Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2abdec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

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

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E3.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

0 references

Q11091

Defining formula

${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C2.S8.SS4.p5.m4aadec

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

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4611&oldid=63208"