DLMF:28.28.E13 (Q8437)

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Language	Label	Description	Also known as
English	DLMF:28.28.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{2\mathrm{i}h\cosh z\cosh t}% \sinh z\sinh t\mathrm{Fe}_{m}\left(t,h^{2}\right)\mathrm{d}t=-\dfrac{\pi}{4h}{% \mathrm{i}^{m}}\mathrm{fe}_{m}'\left(0,h^{2}\right){\mathrm{Mc}^{(3)}_{m}}% \left(z,h\right),}}

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DLMF:28.28.E13

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second solution, Mathieu’s equation

Defining formula

{\displaystyle{\displaystyle\mathrm{fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

C28.S5.E1.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2akdec

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Defining formula

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

C1.S4.SS4.m1aidec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aidec

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hyperbolic cosine function

Defining formula

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

C4.S28.E2.m2addec

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hyperbolic sine function

Defining formula

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

C4.S28.E1.m2abdec

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Defining formula

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

C1.S9.E1.m2ajdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aidec

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modified Mathieu function

Defining formula

{\displaystyle{\displaystyle\mathrm{Fe}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}}

C28.S20.E6.m2adec

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radial Mathieu function

Defining formula

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

C28.S20.E15.m2abdec

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Defining formula

{\displaystyle{\displaystyle m}}

C28.S1.XMD1.m1dec

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Defining formula

{\displaystyle{\displaystyle h}}

C28.S1.XMD11.m1jdec

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Sitelinks

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