DLMF:10.66.E1 (Q3843)

From DRMF

Revision as of 14:24, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:10.66.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{ber}_{\nu}x+i\operatorname{bei}_{\nu% }x=\sum_{k=0}^{\infty}\frac{e^{(3\nu+k)\pi i/4}x^{k}J_{\nu+k}\left(x\right)}{2% ^{k/2}k!}=\sum_{k=0}^{\infty}\frac{e^{(3\nu+3k)\pi i/4}x^{k}I_{\nu+k}\left(x% \right)}{2^{k/2}k!}.}}

0 references

DLMF:10.66.E1

0 references

Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2adec

0 references

Kelvin function

Defining formula

{\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C10.S61.E1.m3adec

0 references

Kelvin function

Defining formula

{\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C10.S61.E1.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

0 references

Defining formula

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

C1.S9.E1.m2adec

0 references

modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C10.S1.XMD4.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1dec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3843&oldid=46733"