DLMF:13.14.E12 (Q4501): Difference between revisions

From DRMF

Jump to navigation Jump to search

Revision as of 15:28, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 16:06, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(12 intermediate revisions by the same user not shown)
		Property / Symbols used
			Whittaker confluent hypergeometric function
		Property / Symbols used: Whittaker confluent hypergeometric function / rank
			Normal rank
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$ \WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			xml-id: C13.S14.E2.m2afdec
		Property / Symbols used
			Whittaker confluent hypergeometric function
		Property / Symbols used: Whittaker confluent hypergeometric function / rank
			Normal rank
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$ \WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			xml-id: C13.S14.E3.m2addec
		Property / Symbols used
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2abdec
		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.m2ajdec
		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.m2abdec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2adec
		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2abdec
		Property / Symbols used
			Q11557
		Property / Symbols used: Q11557 / rank
			Normal rank
		Property / Symbols used: Q11557 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11557 / qualifier
			xml-id: C13.S1.XMD6.m1kdec
		Property / Symbols used
			Q11561
		Property / Symbols used: Q11561 / rank
			Normal rank
		Property / Symbols used: Q11561 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11561 / qualifier
			xml-id: C13.S1.XMD1.m1adec

---

Latest revision as of 16:06, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.14.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle W_{\kappa,\mu}\left(ze^{2m\pi\mathrm{i}}\right)=\frac{(-1)^{m+1}2\pi\mathrm{i}\sin\left(2\pi\mu m\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)\Gamma\left(1+2\mu\right)\sin\left(2\pi\mu\right)}M_{\kappa,\mu}\left(z\right)+(-1)^{m}e^{-2m\mu\pi\mathrm{i}}W_{\kappa,\mu}\left(z\right).}}$

0 references

DLMF id

DLMF:13.14.E12

0 references

Symbols used

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E2.m2afdec

0 references

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E3.m2addec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2abdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2ajdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2abdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2adec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

0 references

Q11557

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C13.S1.XMD6.m1kdec

0 references

Q11561

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C13.S1.XMD1.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4501&oldid=62581"