DLMF:28.28.E28 (Q8455): Difference between revisions

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Revision as of 15:26, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:26, 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
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2aqdec
		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.m3audec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2afdec
		Property / Symbols used
			Q12284
		Property / Symbols used: Q12284 / rank
			Normal rank
		Property / Symbols used: Q12284 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q12284 / qualifier
			xml-id: C28.S1.XMD1.m1idec
		Property / Symbols used
			Q12294
		Property / Symbols used: Q12294 / rank
			Normal rank
		Property / Symbols used: Q12294 / qualifier
			Defining formula: ${\displaystyle{\displaystyle h}}$ h
		Property / Symbols used: Q12294 / qualifier
			xml-id: C28.S1.XMD11.m1wdec
		Property / Symbols used
			Q12278
		Property / Symbols used: Q12278 / rank
			Normal rank
		Property / Symbols used: Q12278 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q12278 / qualifier
			xml-id: C28.S1.XMD7.m1jdec
		Property / Symbols used
			DLMF:28.28.E27
		Property / Symbols used: DLMF:28.28.E27 / rank
			Normal rank
		Property / Symbols used: DLMF:28.28.E27 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\alpha^{(s)}_{\nu,m}}}$ \alpha^{(s)}_{\nu,m}
		Property / Symbols used: DLMF:28.28.E27 / qualifier
			xml-id: C28.S28.XMD7.m1cdec

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Latest revision as of 15:26, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:28.28.E28	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\alpha^{(1)}_{\nu,m}=\dfrac{1}{2\pi}\int_{0}^{2\pi}\sin t\mathrm{me}_{\nu}\left(t,h^{2}\right)\mathrm{me}_{-\nu-2m-1}\left(t,h^{2}\right)\mathrm{d}t=(-1)^{m+1}\dfrac{2\mathrm{i}}{\pi}\dfrac{\mathrm{me}_{\nu}'\left(0,h^{2}\right)\mathrm{me}_{-\nu-2m-1}\left(0,h^{2}\right)}{h\mathrm{D}_{1}\left(\nu,\nu+2m+1,0\right)}.}}$

0 references

DLMF id

DLMF:28.28.E28

0 references

Symbols used

Q12317

Defining formula

${\displaystyle{\displaystyle\mathrm{D}_{\NVar{j}}\left(\NVar{\nu},\NVar{\mu},\NVar{z}\right)}}$

xml-id

C28.S28.E24.m1addec

0 references

Q12299

Defining formula

${\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$

xml-id

C28.S12.SS2.p2.m2agdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2awdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1audec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aqdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3audec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2afdec

0 references

Q12284

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C28.S1.XMD1.m1idec

0 references

Q12294

Defining formula

${\displaystyle{\displaystyle h}}$

xml-id

C28.S1.XMD11.m1wdec

0 references

Q12278

Defining formula

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

xml-id

C28.S1.XMD7.m1jdec

0 references

DLMF:28.28.E27

Defining formula

${\displaystyle{\displaystyle\alpha^{(s)}_{\nu,m}}}$

xml-id

C28.S28.XMD7.m1cdec

0 references

 

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