DLMF:28.28.E14 (Q8438): Difference between revisions

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Revision as of 15:21, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:21, 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
			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.m3ajdec
		Property / Symbols used
			modified Mathieu function
		Property / Symbols used: modified Mathieu function / rank
			Normal rank
		Property / Symbols used: modified Mathieu function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{Ge}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)}}$ \modMathieuGe{\NVar{n}}@{\NVar{z}}{\NVar{q}}
		Property / Symbols used: modified Mathieu function / qualifier
			xml-id: C28.S20.E7.m2adec
		Property / Symbols used
			radial Mathieu function
		Property / Symbols used: radial Mathieu function / rank
			Normal rank
		Property / Symbols used: radial Mathieu function / qualifier
			Defining formula: ${\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)}}$ \radMathieuMs{\NVar{j}}{\NVar{n}}@{\NVar{z}}{\NVar{h}}
		Property / Symbols used: radial Mathieu function / qualifier
			xml-id: C28.S20.E16.m2abdec
		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.m1adec
		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.m1kdec
		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.m1ldec

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Latest revision as of 15:21, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:28.28.E14	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{2\mathrm{i}h\cosh z\cosh t}\mathrm{Ge}_{m}\left(t,h^{2}\right)\mathrm{d}t=\tfrac{1}{2}\pi{\mathrm{i}^{m+1}}\mathrm{ge}_{m}\left(0,h^{2}\right){\mathrm{Ms}^{(3)}_{m}}\left(z,h\right).}}$

0 references

DLMF id

DLMF:28.28.E14

0 references

Symbols used

second solution, Mathieu’s equation

Defining formula

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

xml-id

C28.S5.E2.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aldec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1ajdec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2ajdec

0 references

hyperbolic cosine function

Defining formula

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

xml-id

C4.S28.E2.m2aedec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2akdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3ajdec

0 references

modified Mathieu function

Defining formula

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

xml-id

C28.S20.E7.m2adec

0 references

radial Mathieu function

Defining formula

${\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z},\NVar{h}\right)}}$

xml-id

C28.S20.E16.m2abdec

0 references

Q12284

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C28.S1.XMD1.m1adec

0 references

Q12294

Defining formula

${\displaystyle{\displaystyle h}}$

xml-id

C28.S1.XMD11.m1kdec

0 references

Q12272

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C28.S1.XMD6.m1ldec

0 references

 

Sitelinks

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