DLMF:23.15.E9 (Q7339): Difference between revisions

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		Property / Symbols used
			Q12066
		Property / Symbols used: Q12066 / rank
			Normal rank
		Property / Symbols used: Q12066 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q12066 / qualifier
			xml-id: C23.S1.XMD10.m1edec
		Property / Symbols used
			Q12068
		Property / Symbols used: Q12068 / rank
			Normal rank
		Property / Symbols used: Q12068 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tau}}$ \tau
		Property / Symbols used: Q12068 / qualifier
			xml-id: C23.S1.XMD9.m1ddec

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Latest revision as of 01:19, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:23.15.E9	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\eta\left(\tau\right)=\left(\tfrac{1}{2}\theta_{1}'\left(0,q\right)\right)^{1/3}=e^{i\pi\tau/12}\theta_{3}\left(\tfrac{1}{2}\pi(1+\tau)\middle|3\tau\right).}}$

0 references

DLMF id

DLMF:23.15.E9

0 references

Symbols used

Dedekind’s eta function (or Dedekind modular function)

Defining formula

${\displaystyle{\displaystyle\eta\left(\NVar{\tau}\right)}}$

xml-id

C27.S14.E12.m2adec

0 references

Q11945

Defining formula

${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}$

xml-id

C20.S2.SS1.m2addec

0 references

Q11946

Defining formula

${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)}}$

xml-id

C20.S2.SS1.m1adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q12066

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C23.S1.XMD10.m1edec

0 references

Q12068

Defining formula

${\displaystyle{\displaystyle\tau}}$

xml-id

C23.S1.XMD9.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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