DLMF:18.10.E4 (Q5628)

From DRMF

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:18.10.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\frac{P^{(\alpha,\alpha)}_{n}\left(\cos\theta% \right)}{P^{(\alpha,\alpha)}_{n}\left(1\right)}=\frac{C^{(\alpha+\frac{1}{2})}% _{n}\left(\cos\theta\right)}{C^{(\alpha+\frac{1}{2})}_{n}\left(1\right)}}=% \frac{\Gamma\left(\alpha+1\right)}{\pi^{\frac{1}{2}}\Gamma{(\alpha+\tfrac{1}{2% })}}\*{\int_{0}^{\pi}(\cos\theta+i\sin\theta\cos\phi)^{n}\*(\sin\phi)^{2\alpha% }\mathrm{d}\phi},}}

0 references

DLMF:18.10.E4

0 references

{\displaystyle{\displaystyle\alpha>-\frac{1}{2}}}

0 references

Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2abdec

0 references

Defining formula

{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

C18.S3.T1.t1.r2.m2abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

0 references

cosine function

Defining formula

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

C4.S14.E2.m2acdec

0 references

Defining formula

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

C1.S4.SS4.m1acdec

0 references

Defining formula

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

C1.S9.E1.m2aadec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3acdec

0 references

Defining formula

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

C4.S14.E1.m2abdec

0 references

Defining formula

{\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r3.m2aadec

0 references

Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1cdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5628&oldid=57834"