DLMF:18.15.E22 (Q5717)

From DRMF

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:18.15.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(\nu x\right)=(-1)^{n}\frac{% e^{\frac{1}{2}\nu x}}{2^{\alpha-\frac{1}{2}}x^{\frac{1}{2}\alpha+\frac{1}{4}}}% \*\left(\frac{\zeta}{x-1}\right)^{\frac{1}{4}}\left(\frac{\mathrm{Ai}\left(\nu% ^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{1}{3}}}\sum_{m=0}^{M-1}\frac{E_{m}(% \zeta)}{\nu^{2m}}+\frac{\mathrm{Ai}'\left(\nu^{\frac{2}{3}}\zeta\right)}{\nu^{% \frac{5}{3}}}\sum_{m=0}^{M-1}\frac{F_{m}(\zeta)}{\nu^{2m}}+\mathrm{envAi}\left% (\nu^{\frac{2}{3}}\zeta\right)O\left(\frac{1}{\nu^{2M-\frac{2}{3}}}\right)% \right),}}

0 references

DLMF:18.15.E22

0 references

Defining formula

{\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}

C9.S2.SS1.m1adec

0 references

order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2afdec

0 references

Defining formula

{\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r12.m2abdec

0 references

Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11adec

0 references

Defining formula

{\displaystyle{\displaystyle\mathrm{envAi}\left(\NVar{x}\right)}}

C2.S8.SS3.p4.m4adec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2abdec

0 references

Defining formula

{\displaystyle{\displaystyle m}}

C18.S1.XMD5.m1ndec

0 references

Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1mdec

0 references

Defining formula

{\displaystyle{\displaystyle\nu}}

C18.S15.XMD14.m1bdec

0 references

Defining formula

{\displaystyle{\displaystyle\zeta}}

C18.S15.XMD18.m1adec

0 references

Defining formula

{\displaystyle{\displaystyle E_{m}}}

C18.S15.XMD19.m1dec

0 references

coefficient (locally)

Defining formula

{\displaystyle{\displaystyle F_{m}}}

C18.S15.XMD20.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1gdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5717&oldid=59805"