DLMF:12.14.E32 (Q4274): Difference between revisions

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Revision as of 15:32, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:32, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\phi(\zeta)}}$ \phi(\zeta)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C12.S10.XMD22.m1adec
		Property / Symbols used
			Q11535
		Property / Symbols used: Q11535 / rank
			Normal rank
		Property / Symbols used: Q11535 / qualifier
			Defining formula: ${\displaystyle{\displaystyle A_{s}(\zeta)}}$ A_{s}(\zeta)
		Property / Symbols used: Q11535 / qualifier
			xml-id: C12.S10.XMD23.m1dec
		Property / Symbols used
			Q11536
		Property / Symbols used: Q11536 / rank
			Normal rank
		Property / Symbols used: Q11536 / qualifier
			Defining formula: ${\displaystyle{\displaystyle B_{s}(\zeta)}}$ B_{s}(\zeta)
		Property / Symbols used: Q11536 / qualifier
			xml-id: C12.S10.XMD24.m1dec
		Property / Symbols used
			DLMF:12.14.E28
		Property / Symbols used: DLMF:12.14.E28 / rank
			Normal rank
		Property / Symbols used: DLMF:12.14.E28 / qualifier
			Defining formula: ${\displaystyle{\displaystyle l(\mu)}}$ l(\mu)
		Property / Symbols used: DLMF:12.14.E28 / qualifier
			xml-id: C12.S14.XMD13.m1edec

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Latest revision as of 15:32, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:12.14.E32	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle W\left(\tfrac{1}{2}\mu^{2},\mu t\sqrt{2}\right)\sim\frac{\pi^{\frac{1}{2}}\mu^{\frac{1}{3}}l(\mu)}{2^{\frac{1}{2}}e^{\frac{1}{4}\pi\mu^{2}}}\phi(\zeta)\left(\mathrm{Bi}\left(-\mu^{\frac{4}{3}}\zeta\right)\sum_{s=0}^{\infty}(-1)^{s}\frac{A_{s}(\zeta)}{\mu^{4s}}+\frac{\mathrm{Bi}'\left(-\mu^{\frac{4}{3}}\zeta\right)}{\mu^{\frac{8}{3}}}\sum_{s=0}^{\infty}(-1)^{s}\frac{B_{s}(\zeta)}{\mu^{4s}}\right),}}$

0 references

DLMF id

DLMF:12.14.E32

0 references

Symbols used

Q11081

Defining formula

${\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}$

xml-id

C9.S2.SS1.m2adec

0 references

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11agdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2akdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2ahdec

0 references

Q11543

Defining formula

${\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}$

xml-id

C12.S14.SS1.p1.m1apdec

0 references

Q11526

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C12.S1.XMD5.m1edec

0 references

Q11534

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C12.S10.XMD21.m1dec

0 references

function (locally)

Defining formula

${\displaystyle{\displaystyle\phi(\zeta)}}$

xml-id

C12.S10.XMD22.m1adec

0 references

Q11535

Defining formula

${\displaystyle{\displaystyle A_{s}(\zeta)}}$

xml-id

C12.S10.XMD23.m1dec

0 references

Q11536

Defining formula

${\displaystyle{\displaystyle B_{s}(\zeta)}}$

xml-id

C12.S10.XMD24.m1dec

0 references

DLMF:12.14.E28

Defining formula

${\displaystyle{\displaystyle l(\mu)}}$

xml-id

C12.S14.XMD13.m1edec

0 references

 

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