DLMF:12.9.E3 (Q4152)

From DRMF

Revision as of 15:16, 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:12.9.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle U\left(a,z\right)\sim e^{-\frac{1}{4}z^{2}}z^{-a-% \frac{1}{2}}\sum_{s=0}^{\infty}(-1)^{s}\frac{{\left(\frac{1}{2}+a\right)_{2s}}% }{s!(2z^{2})^{s}}\pm i\frac{\sqrt{2\pi}}{\Gamma\left(\tfrac{1}{2}+a\right)}e^{% \mp i\pi a}e^{\frac{1}{4}z^{2}}z^{a-\frac{1}{2}}\sum_{s=0}^{\infty}\frac{{% \left(\tfrac{1}{2}-a\right)_{2s}}}{s!(2z^{2})^{s}},}}

0 references

DLMF:12.9.E3

0 references

{\displaystyle{\displaystyle\tfrac{1}{4}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{5}{4}\pi-\delta}}

0 references

Defining formula

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

C5.S2.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1abdec

0 references

Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2abdec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2abdec

0 references

Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5abdec

0 references

Defining formula

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

C1.S9.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

C12.S2.SS1.p1.m1aadec

0 references

Defining formula

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

C1.S9.E7.m1abdec

0 references

Defining formula

{\displaystyle{\displaystyle z}}

C12.S1.XMD3.m1bdec

0 references

Defining formula

{\displaystyle{\displaystyle s}}

C12.S1.XMD5.m1bdec

0 references

Defining formula

{\displaystyle{\displaystyle a}}

C12.S1.XMD6.m1bdec

0 references

Defining formula

{\displaystyle{\displaystyle\delta}}

C12.S1.XMD8.m1bdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4152&oldid=56099"