DLMF:10.50.E4 (Q3734): Difference between revisions

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Revision as of 14:12, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:12, 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
			spherical Bessel function of the first kind
		Property / Symbols used: spherical Bessel function of the first kind / rank
			Normal rank
		Property / Symbols used: spherical Bessel function of the first kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}$ \sphBesselJ{\NVar{n}}@{\NVar{z}}
		Property / Symbols used: spherical Bessel function of the first kind / qualifier
			xml-id: C10.S47.E3.m2abdec
		Property / Symbols used
			spherical Bessel function of the second kind
		Property / Symbols used: spherical Bessel function of the second kind / rank
			Normal rank
		Property / Symbols used: spherical Bessel function of the second kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)}}$ \sphBesselY{\NVar{n}}@{\NVar{z}}
		Property / Symbols used: spherical Bessel function of the second kind / qualifier
			xml-id: C10.S47.E4.m2abdec
		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.m1cdec
		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.m1dec
		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
			expansion (locally)
		Property / Symbols used: expansion (locally) / rank
			Normal rank
		Property / Symbols used: expansion (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle a_{k}(\nu)}}$ a_{k}(\nu)
		Property / Symbols used: expansion (locally) / qualifier
			xml-id: C10.S17.XMD1.m1dec

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Latest revision as of 14:12, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.50.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathsf{j}_{0}\left(z\right)\mathsf{j}_{n}\left(z\right)+\mathsf{y}_{0}\left(z\right)\mathsf{y}_{n}\left(z\right)=\cos\left(\tfrac{1}{2}n\pi\right)\sum_{k=0}^{\left\lfloor n/2\right\rfloor}(-1)^{k}\frac{a_{2k}(n+\tfrac{1}{2})}{z^{2k+2}}+\sin\left(\tfrac{1}{2}n\pi\right)\sum_{k=0}^{\left\lfloor(n-1)/2\right\rfloor}(-1)^{k}\frac{a_{2k+1}(n+\tfrac{1}{2})}{z^{2k+3}},}}$

0 references

DLMF id

DLMF:10.50.E4

0 references

Symbols used

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2adec

0 references

Q11169

Defining formula

${\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}$

xml-id

introduction.Sx4.p1.t1.r17.m4adec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2adec

0 references

spherical Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}$

xml-id

C10.S47.E3.m2abdec

0 references

spherical Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)}}$

xml-id

C10.S47.E4.m2abdec

0 references

Q11429

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C10.S1.XMD2.m1cdec

0 references

Q11428

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C10.S1.XMD3.m1dec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1cdec

0 references

expansion (locally)

Defining formula

${\displaystyle{\displaystyle a_{k}(\nu)}}$

xml-id

C10.S17.XMD1.m1dec

0 references

 

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