DLMF:28.28.E48 (Q8479): Difference between revisions

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Revision as of 15:33, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:33, 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
			Q12283
		Property / Symbols used: Q12283 / rank
			Normal rank
		Property / Symbols used: Q12283 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$ \Mathieuce{\NVar{n}}@{\NVar{z}}{\NVar{q}}
		Property / Symbols used: Q12283 / qualifier
			xml-id: C28.S2.SS6.p1.m7andec
		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.m2aandec
		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.m1aaldec
		Property / Symbols used
			hyperbolic cosine function
		Property / Symbols used: hyperbolic cosine function / rank
			Normal rank
		Property / Symbols used: hyperbolic cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cosh\NVar{z}}}$ \cosh@@{\NVar{z}}
		Property / Symbols used: hyperbolic cosine function / qualifier
			xml-id: C4.S28.E2.m2andec
		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.m2apdec
		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.m2aahdec
		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.m3aakdec
		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.m2atdec
		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.m1acdec
		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.m1aqdec
		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.m1sdec
		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.m1akdec
		Property / Symbols used
			DLMF:28.28.E49
		Property / Symbols used: DLMF:28.28.E49 / rank
			Normal rank
		Property / Symbols used: DLMF:28.28.E49 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\widehat{\alpha}_{n,m}}}$ \widehat{\alpha}_{n,m}
		Property / Symbols used: DLMF:28.28.E49 / qualifier
			xml-id: C28.S28.XMD11.m1ddec

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Latest revision as of 15:33, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:28.28.E48	No description defined

Statements

Defining formula

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

0 references

DLMF id

DLMF:28.28.E48

0 references

Symbols used

Q12320

Defining formula

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

xml-id

C28.S28.E39.m1abdec

0 references

Q12283

Defining formula

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

xml-id

C28.S2.SS6.p1.m7andec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aandec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aaldec

0 references

hyperbolic cosine function

Defining formula

${\displaystyle{\displaystyle\cosh\NVar{z}}}$

xml-id

C4.S28.E2.m2andec

0 references

hyperbolic sine function

Defining formula

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

xml-id

C4.S28.E1.m2apdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aahdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aakdec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2atdec

0 references

Q12284

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C28.S1.XMD1.m1acdec

0 references

Q12294

Defining formula

${\displaystyle{\displaystyle h}}$

xml-id

C28.S1.XMD11.m1aqdec

0 references

Q12279

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C28.S1.XMD2.m1sdec

0 references

Q12272

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C28.S1.XMD6.m1akdec

0 references

DLMF:28.28.E49

Defining formula

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

xml-id

C28.S28.XMD11.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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