DLMF:14.9.E1 (Q4791)

From DRMF

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:14.9.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{\pi\sin\left(\mu\pi\right)}{2\Gamma\left(\nu% -\mu+1\right)}\mathsf{P}^{-\mu}_{\nu}\left(x\right)=-\frac{1}{\Gamma\left(\nu+% \mu+1\right)}\mathsf{Q}^{\mu}_{\nu}\left(x\right)+\frac{\cos\left(\mu\pi\right% )}{\Gamma\left(\nu-\mu+1\right)}\mathsf{Q}^{-\mu}_{\nu}\left(x\right).}}

0 references

DLMF:14.9.E1

0 references

Defining formula

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

C5.S2.E1.m2adec

0 references

Ferrers function of the first kind

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E1.m2adec

0 references

Ferrers function of the second kind

Defining formula

{\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E2.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

0 references

cosine function

Defining formula

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

C4.S14.E2.m2adec

0 references

Defining formula

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

C4.S14.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1dec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4791&oldid=32831"