DLMF:10.9.E6 (Q3071): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit Newer edit →

Revision as of 15:12, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.9.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}% \cos\left(z\sin\theta-\nu\theta\right)\mathrm{d}\theta-\frac{\sin\left(\nu\pi% \right)}{\pi}\int_{0}^{\infty}e^{-z\sinh t-\nu t}\mathrm{d}t,}}

0 references

DLMF:10.9.E6

0 references

{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}

0 references

Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2acdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

0 references

cosine function

Defining formula

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

C4.S14.E2.m2addec

0 references

Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aedec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2abdec

0 references

hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aedec

0 references

Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1aadec

0 references

Defining formula

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

C4.S14.E1.m2aedec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3071&oldid=55383"