Mathematical Research Data Initiative
Main page
Recent changes
Random page
Help about MediaWiki
Create a new Item
Create a new Property
Create a new EntitySchema
Merge two items
In other projects
Discussion
View source
View history
Purge
English
Log in

Formula:4348

From MaRDI portal
Jump to:navigation, search

Digital Library of Mathematical Functions ID 10.44.E3

𝒡 Ξ½ ⁑ ( u Β± v ) = βˆ‘ k = - ∞ ∞ ( Β± 1 ) k ⁒ 𝒡 Ξ½ + k ⁑ ( u ) ⁒ I k ⁑ ( v ) , modified-cylinder-function 𝜈 plus-or-minus 𝑒 𝑣 superscript subscript π‘˜ superscript plus-or-minus 1 π‘˜ modified-cylinder-function 𝜈 π‘˜ 𝑒 modified-Bessel-first-kind π‘˜ 𝑣 {\displaystyle{\displaystyle\mathscr{Z}_{\nu}\left(u\pm v\right)=\sum_{k=-% \infty}^{\infty}(\pm 1)^{k}\mathscr{Z}_{\nu+k}\left(u\right)I_{k}\left(v\right% ),}}


Constraint(s)

| v | < | u | 𝑣 𝑒 {\displaystyle{\displaystyle|v|<|u|}}

Symbols List

  • I Ξ½ ⁑ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}} : modified Bessel function of the first kind
  • 𝒡 Ξ½ ⁑ ( z ) modified-cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{Z}_{\NVar{\nu}}\left(\NVar{z}\right)}} : modified cylinder function
  • k π‘˜ {\displaystyle{\displaystyle k}} : nonnegative integer
  • Ξ½ 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  •  Edit this on Wikidata

Resources that cite this formula

No records found.

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Formula:4348&oldid=24166946"
Tools
What links here
Related changes
Special pages
Printable version
Permanent link
Page information
MaRDI portal item
This page was last edited on 3 March 2024, at 02:59.
Privacy policy
About MaRDI portal
Disclaimers
Imprint
Powered by MediaWiki