DLMF:18.14.E3 (Q5666)

From DRMF

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:18.14.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(\tfrac{1}{2}(1-x)\right)^{\frac{1}{2}\alpha+% \frac{1}{4}}\left(\tfrac{1}{2}(1+x)\right)^{\frac{1}{2}\beta+\frac{1}{4}}|P^{(% \alpha,\beta)}_{n}\left(x\right)|\leq\frac{\Gamma\left(\max(\alpha,\beta)+n+1% \right)}{\pi^{\frac{1}{2}}n!\left(n+\tfrac{1}{2}(\alpha+\beta+1)\right)^{\max(% \alpha,\beta)+\frac{1}{2}}},}}

0 references

DLMF:18.14.E3

0 references

{\displaystyle{\displaystyle-\tfrac{1}{2}\leq\beta\leq\tfrac{1}{2}}}

0 references

Defining formula

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

C5.S2.E1.m2adec

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.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5abdec

0 references

Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1bdec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1bdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5666&oldid=58910"