DLMF:14.17.E16 (Q4897): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:14.17.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{-1}^{1}\mathsf{P}^{m}_{l}\left(x\right)% \mathsf{Q}^{m}_{n}\left(x\right)\mathrm{d}x=\frac{\left(1-(-1)^{l+n}\right)(l+% m)!}{(l-n)(l+n+1)(l-m)!},}}

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DLMF:14.17.E16

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{\displaystyle{\displaystyle l\neq n}}

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Ferrers function of the first kind

Defining formula

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

C14.S3.E1.m2aidec

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Ferrers function of the second kind

Defining formula

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

C14.S3.E2.m2abdec

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Defining formula

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

C1.S4.SS4.m1aodec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5abdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aodec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1odec

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Defining formula

{\displaystyle{\displaystyle m}}

C14.S1.XMD5.m1ddec

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Defining formula

{\displaystyle{\displaystyle n}}

C14.S1.XMD6.m1ddec

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