DLMF:28.28.E45 (Q8476): Difference between revisions

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Revision as of 15:32, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:32, 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.m2aakdec
		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.m1aaidec
		Property / Symbols used
			hyperbolic sine function
		Property / Symbols used: hyperbolic sine function / rank
			Normal rank
		Property / Symbols used: hyperbolic sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sinh\NVar{z}}}$ \sinh@@{\NVar{z}}
		Property / Symbols used: hyperbolic sine function / qualifier
			xml-id: C4.S28.E1.m2andec
		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.m2aaedec
		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.m3aahdec
		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.m2ardec
		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.m1zdec
		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.m1andec
		Property / Symbols used
			Q12279
		Property / Symbols used: Q12279 / rank
			Normal rank
		Property / Symbols used: Q12279 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q12279 / qualifier
			xml-id: C28.S1.XMD2.m1pdec
		Property / Symbols used
			Q12272
		Property / Symbols used: Q12272 / rank
			Normal rank
		Property / Symbols used: Q12272 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q12272 / qualifier
			xml-id: C28.S1.XMD6.m1aidec
		Property / Symbols used
			DLMF:28.28.E46
		Property / Symbols used: DLMF:28.28.E46 / rank
			Normal rank
		Property / Symbols used: DLMF:28.28.E46 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\widehat{\gamma}_{n,m}}}$ \widehat{\gamma}_{n,m}
		Property / Symbols used: DLMF:28.28.E46 / qualifier
			xml-id: C28.S28.XMD10.m1adec

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Latest revision as of 15:32, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:28.28.E45	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\dfrac{\sinh\left(2z\right)}{\pi^{2}}\int_{0}^{2\pi}\dfrac{\mathrm{se}_{n}'\left(t,h^{2}\right)\mathrm{ce}_{m}\left(t,h^{2}\right)}{{\sinh^{2}}z+{\sin^{2}}t}\mathrm{d}t=(-1)^{p+1}\mathrm{i}\widehat{\gamma}_{n,m}\mathrm{Dsc}_{1}\left(n,m,z\right),}}$

0 references

DLMF id

DLMF:28.28.E45

0 references

Symbols used

Q12319

Defining formula

${\displaystyle{\displaystyle\mathrm{Dsc}_{\NVar{j}}\left(\NVar{n},\NVar{m},\NVar{z}\right)}}$

xml-id

C28.S28.E40.m1aedec

0 references

Q12283

Defining formula

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

xml-id

C28.S2.SS6.p1.m7akdec

0 references

Q12286

Defining formula

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

xml-id

C28.S2.SS6.p1.m8aldec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aakdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aaidec

0 references

hyperbolic sine function

Defining formula

${\displaystyle{\displaystyle\sinh\NVar{z}}}$

xml-id

C4.S28.E1.m2andec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aaedec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aahdec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2ardec

0 references

Q12284

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C28.S1.XMD1.m1zdec

0 references

Q12294

Defining formula

${\displaystyle{\displaystyle h}}$

xml-id

C28.S1.XMD11.m1andec

0 references

Q12279

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C28.S1.XMD2.m1pdec

0 references

Q12272

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C28.S1.XMD6.m1aidec

0 references

DLMF:28.28.E46

Defining formula

${\displaystyle{\displaystyle\widehat{\gamma}_{n,m}}}$

xml-id

C28.S28.XMD10.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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