DLMF:28.28.E30 (Q8457)

From DRMF

Revision as of 15:27, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:28.28.E30	No description defined

Statements

Defining formula

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

0 references

DLMF:28.28.E30

0 references

Defining formula

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

C28.S28.E24.m1afdec

0 references

Defining formula

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

C28.S12.SS2.p2.m2aidec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aydec

0 references

cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2ahdec

0 references

Defining formula

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

C1.S4.SS4.m1awdec

0 references

hyperbolic sine function

Defining formula

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

C4.S28.E1.m2afdec

0 references

Defining formula

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

C1.S9.E1.m2asdec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3awdec

0 references

Defining formula

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

C4.S14.E1.m2ahdec

0 references

Defining formula

{\displaystyle{\displaystyle m}}

C28.S1.XMD1.m1kdec

0 references

Defining formula

{\displaystyle{\displaystyle h}}

C28.S1.XMD11.m1ydec

0 references

Defining formula

{\displaystyle{\displaystyle z}}

C28.S1.XMD6.m1xdec

0 references

Defining formula

{\displaystyle{\displaystyle\nu}}

C28.S1.XMD7.m1ldec

0 references

Defining formula

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

C28.S28.XMD7.m1edec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8457&oldid=57878"