Difference between revisions of "DLMF:31.2.E8 (Q8989)"

From DRMF

Jump to navigation Jump to search

Revision as of 11:26, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 11:27, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
(7 intermediate revisions by the same user not shown)
		Property / Symbols used
		+	Q12458
		Property / Symbols used: Q12458 / rank
		+	Normal rank
		Property / Symbols used: Q12458 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\gamma}}$ \gamma
		Property / Symbols used: Q12458 / qualifier
		+	xml-id: C31.S1.XMD10.m1ddec
		Property / Symbols used
		+	Q12459
		Property / Symbols used: Q12459 / rank
		+	Normal rank
		Property / Symbols used: Q12459 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\delta}}$ \delta
		Property / Symbols used: Q12459 / qualifier
		+	xml-id: C31.S1.XMD11.m1ddec
		Property / Symbols used
		+	Q12460
		Property / Symbols used: Q12460 / rank
		+	Normal rank
		Property / Symbols used: Q12460 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\epsilon}}$ \epsilon
		Property / Symbols used: Q12460 / qualifier
		+	xml-id: C31.S1.XMD12.m1ddec
		Property / Symbols used
		+	Q12462
		Property / Symbols used: Q12462 / rank
		+	Normal rank
		Property / Symbols used: Q12462 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q12462 / qualifier
		+	xml-id: C31.S1.XMD7.m1cdec
		Property / Symbols used
		+	Q12463
		Property / Symbols used: Q12463 / rank
		+	Normal rank
		Property / Symbols used: Q12463 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\alpha}}$ \alpha
		Property / Symbols used: Q12463 / qualifier
		+	xml-id: C31.S1.XMD8.m1cdec
		Property / Symbols used
		+	Q12464
		Property / Symbols used: Q12464 / rank
		+	Normal rank
		Property / Symbols used: Q12464 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\beta}}$ \beta
		Property / Symbols used: Q12464 / qualifier
		+	xml-id: C31.S1.XMD9.m1cdec
		Property / Symbols used
		+	Q12471
		Property / Symbols used: Q12471 / rank
		+	Normal rank
		Property / Symbols used: Q12471 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\zeta}}$ \zeta
		Property / Symbols used: Q12471 / qualifier
		+	xml-id: C31.S2.XMD10.m1adec
		Property / Symbols used
		+	Q12472
		Property / Symbols used: Q12472 / rank
		+	Normal rank
		Property / Symbols used: Q12472 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q12472 / qualifier
		+	xml-id: C31.S2.XMD9.m1adec

---

Latest revision as of 11:27, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:31.2.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\zeta}^{2}}+\left((2\gamma-1)\frac{\operatorname{cn}\zeta\operatorname{dn}\zeta}{\operatorname{sn}\zeta}-(2\delta-1)\frac{\operatorname{sn}\zeta\operatorname{dn}\zeta}{\operatorname{cn}\zeta}-(2\epsilon-1)k^{2}\frac{\operatorname{sn}\zeta\operatorname{cn}\zeta}{\operatorname{dn}\zeta}\right)\frac{\mathrm{d}w}{\mathrm{d}\zeta}+4k^{2}(\alpha\beta{\operatorname{sn}^{2}}\zeta-q)w=0.}}$

0 references

DLMF id

DLMF:31.2.E8

0 references

Symbols used

Jacobian elliptic function

Defining formula

${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$

xml-id

C22.S2.E5.m2adec

0 references

Jacobian elliptic function

Defining formula

${\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}$

xml-id

C22.S2.E6.m2adec

0 references

Jacobian elliptic function

Defining formula

${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$

xml-id

C22.S2.E4.m2aadec

0 references

derivative of $$f$$ with respect to $$x$$

Defining formula

${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$

xml-id

C1.S4.E4.m2acdec

0 references

Q12458

Defining formula

${\displaystyle{\displaystyle\gamma}}$

xml-id

C31.S1.XMD10.m1ddec

0 references

Q12459

Defining formula

${\displaystyle{\displaystyle\delta}}$

xml-id

C31.S1.XMD11.m1ddec

0 references

Q12460

Defining formula

${\displaystyle{\displaystyle\epsilon}}$

xml-id

C31.S1.XMD12.m1ddec

0 references

Q12462

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C31.S1.XMD7.m1cdec

0 references

Q12463

Defining formula

${\displaystyle{\displaystyle\alpha}}$

xml-id

C31.S1.XMD8.m1cdec

0 references

Q12464

Defining formula

${\displaystyle{\displaystyle\beta}}$

xml-id

C31.S1.XMD9.m1cdec

0 references

Q12471

Defining formula

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

xml-id

C31.S2.XMD10.m1adec

0 references

Q12472

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C31.S2.XMD9.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8989&oldid=36582"