DLMF:11.9.E5 (Q4012): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 14:52, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:52, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(3 intermediate revisions by the same user not shown)
		Property / Symbols used
			cosine function
		Property / Symbols used: cosine function / rank
			Normal rank
		Property / Symbols used: cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cos\NVar{z}}}$ \cos@@{\NVar{z}}
		Property / Symbols used: cosine function / qualifier
			xml-id: C4.S14.E2.m2adec
		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
			Q11491
		Property / Symbols used: Q11491 / rank
			Normal rank
		Property / Symbols used: Q11491 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11491 / qualifier
			xml-id: C11.S1.XMD2.m1cdec
		Property / Symbols used
			Q11492
		Property / Symbols used: Q11492 / rank
			Normal rank
		Property / Symbols used: Q11492 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11492 / qualifier
			xml-id: C11.S1.XMD3.m1ddec

---

Latest revision as of 14:52, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:11.9.E5	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle S_{{\mu},{\nu}}\left(z\right)=s_{{\mu},{\nu}}\left(z\right)+2^{\mu-1}\Gamma\left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{2}\right)\Gamma\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}\right)\*\left(\sin\left(\tfrac{1}{2}(\mu-\nu)\pi\right)\,J_{\nu}\left(z\right)-\cos\left(\tfrac{1}{2}(\mu-\nu)\pi\right)\,Y_{\nu}\left(z\right)\right),}}$

0 references

DLMF id

DLMF:11.9.E5

0 references

Symbols defined

Lommel function

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2aadec

0 references

Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E3.m2aadec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

Lommel function

Defining formula

${\displaystyle{\displaystyle s_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right)}}$

xml-id

C11.S9.E3.m2abdec

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

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2adec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2adec

0 references

Q11491

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C11.S1.XMD2.m1cdec

0 references

Q11492

Defining formula

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

xml-id

C11.S1.XMD3.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4012&oldid=51798"