DLMF:29.8.E8 (Q8712): Difference between revisions

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Revision as of 01:23, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:24, 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
			Q11600
		Property / Symbols used: Q11600 / rank
			Normal rank
		Property / Symbols used: Q11600 / qualifier
			Defining formula: ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$ \compellintKk@{\NVar{k}}
		Property / Symbols used: Q11600 / qualifier
			xml-id: C19.S2.E8.m1addec
		Property / Symbols used
			derivative of $$f$$ with respect to $$x$$
		Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
			Normal rank
		Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$ \deriv{\NVar{f}}{\NVar{x}}
		Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
			xml-id: C1.S4.E4.m2abdec
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1acdec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3acdec
		Property / Symbols used
			Q11595
		Property / Symbols used: Q11595 / rank
			Normal rank
		Property / Symbols used: Q11595 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{P}^{0}_{\nu}\left(x\right)}}$ \FerrersP[]{\NVar{\nu}}@{\NVar{x}}=\FerrersP[0]{\nu}@{x}
		Property / Symbols used: Q11595 / qualifier
			xml-id: C14.S2.SS2.p2.m2acdec
		Property / Symbols used
			Q12357
		Property / Symbols used: Q12357 / rank
			Normal rank
		Property / Symbols used: Q12357 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q12357 / qualifier
			xml-id: C29.S1.XMD1.m1bdec
		Property / Symbols used
			Q12382
		Property / Symbols used: Q12382 / rank
			Normal rank
		Property / Symbols used: Q12382 / qualifier
			Defining formula: ${\displaystyle{\displaystyle y}}$ y
		Property / Symbols used: Q12382 / qualifier
			xml-id: C29.S1.XMD5.m1cdec
		Property / Symbols used
			Q12348
		Property / Symbols used: Q12348 / rank
			Normal rank
		Property / Symbols used: Q12348 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q12348 / qualifier
			xml-id: C29.S1.XMD6.m1fdec
		Property / Symbols used
			Q12350
		Property / Symbols used: Q12350 / rank
			Normal rank
		Property / Symbols used: Q12350 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q12350 / qualifier
			xml-id: C29.S1.XMD8.m1fdec
		Property / Symbols used
			Q12351
		Property / Symbols used: Q12351 / rank
			Normal rank
		Property / Symbols used: Q12351 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q12351 / qualifier
			xml-id: C29.S1.XMD9.m1cdec
		Property / Symbols used
			Q12378
		Property / Symbols used: Q12378 / rank
			Normal rank
		Property / Symbols used: Q12378 / qualifier
			Defining formula: ${\displaystyle{\displaystyle w(z)}}$ w(z)
		Property / Symbols used: Q12378 / qualifier
			xml-id: C29.S8.XMD1.m1edec

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Latest revision as of 01:24, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:29.8.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathit{Es}^{2m+1}_{\nu}\left(z_{1},k^{2}\right)\frac{\left.\ifrac{\mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|_{z=K}+\left.\ifrac{\mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|_{z=-K}}{\left.\ifrac{\mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|_{z=0}}=\frac{k^{2}}{k^{\prime}}\operatorname{cn}\left(z_{1},k\right)\int_{-K}^{K}\operatorname{cn}\left(z,k\right)\frac{\mathrm{d}\mathsf{P}_{\nu}\left(y\right)}{\mathrm{d}y}\mathit{Es}^{2m+1}_{\nu}\left(z,k^{2}\right)\mathrm{d}z,}}$

0 references

DLMF id

DLMF:29.8.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.m2aadec

0 references

Q12364

Defining formula

${\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},\NVar{k^{2}}\right)}}$

xml-id

C29.S3.SS4.p1.m6adec

0 references

Q11600

Defining formula

${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$

xml-id

C19.S2.E8.m1addec

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.m2abdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1acdec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3acdec

0 references

Q11595

Defining formula

${\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=\mathsf{P}^{0}_{\nu}\left(x\right)}}$

xml-id

C14.S2.SS2.p2.m2acdec

0 references

Q12357

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C29.S1.XMD1.m1bdec

0 references

Q12382

Defining formula

${\displaystyle{\displaystyle y}}$

xml-id

C29.S1.XMD5.m1cdec

0 references

Q12348

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C29.S1.XMD6.m1fdec

0 references

Q12350

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C29.S1.XMD8.m1fdec

0 references

Q12351

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C29.S1.XMD9.m1cdec

0 references

Q12378

Defining formula

${\displaystyle{\displaystyle w(z)}}$

xml-id

C29.S8.XMD1.m1edec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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