DLMF:10.15.E4 (Q3150): Difference between revisions

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Revision as of 15:24, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:25, 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
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2abdec
		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5abdec
		Property / Symbols used
			partial derivative of $$f$$ with respect to $$x$$
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
			Normal rank
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$ \pderiv{\NVar{f}}{\NVar{x}}
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
			xml-id: C1.S5.E3.m4acdec
		Property / Symbols used
			partial differential of $$x$$
		Property / Symbols used: partial differential of $$x$$ / rank
			Normal rank
		Property / Symbols used: partial differential of $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\partial\NVar{x}}}$ \pdiff{\NVar{x}}
		Property / Symbols used: partial differential of $$x$$ / qualifier
			xml-id: C1.S5.E3.m2acdec
		Property / Symbols used
			Q11429
		Property / Symbols used: Q11429 / rank
			Normal rank
		Property / Symbols used: Q11429 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11429 / qualifier
			xml-id: C10.S1.XMD2.m1adec
		Property / Symbols used
			Q11428
		Property / Symbols used: Q11428 / rank
			Normal rank
		Property / Symbols used: Q11428 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11428 / qualifier
			xml-id: C10.S1.XMD3.m1bdec
		Property / Symbols used
			Q11426
		Property / Symbols used: Q11426 / rank
			Normal rank
		Property / Symbols used: Q11426 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11426 / qualifier
			xml-id: C10.S1.XMD6.m1cdec
		Property / Symbols used
			Q11427
		Property / Symbols used: Q11427 / rank
			Normal rank
		Property / Symbols used: Q11427 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11427 / qualifier
			xml-id: C10.S1.XMD7.m1cdec

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Latest revision as of 15:25, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.15.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\left.\frac{\partial Y_{\nu}\left(z\right)}{\partial\nu}\right|_{\nu=n}=-\frac{\pi}{2}J_{n}\left(z\right)+\frac{n!}{2(\tfrac{1}{2}z)^{n}}\sum_{k=0}^{n-1}\frac{(\tfrac{1}{2}z)^{k}Y_{k}\left(z\right)}{k!(n-k)},}}$

0 references

DLMF id

DLMF:10.15.E4

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2acdec

0 references

Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E3.m2abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2abdec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5abdec

0 references

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

Defining formula

${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$

xml-id

C1.S5.E3.m4acdec

0 references

partial differential of $$x$$

Defining formula

${\displaystyle{\displaystyle\partial\NVar{x}}}$

xml-id

C1.S5.E3.m2acdec

0 references

Q11429

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C10.S1.XMD2.m1adec

0 references

Q11428

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C10.S1.XMD3.m1bdec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1cdec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1cdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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