n-0-1-n-2-n-1-2n-1-p-q-p-q-p-q-

Question Number 215091 by mnjuly1970 last updated on 28/Dec/24

Σ_(n=0) ^∞ (−1)^n (( Γ^( 2) (n+1))/(Γ (2n+1))) = ? −−− β (p ,q ) = (( Γ (p)Γ(q))/(Γ(p+q )))

$$ \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \:\frac{\:\Gamma^{\:\mathrm{2}} \left({n}+\mathrm{1}\right)}{\Gamma\:\left(\mathrm{2}{n}+\mathrm{1}\right)}\:=\:? \\ $$$$\:\:\:\:\:\:−−− \\ $$$$\:\:\:\:\beta\:\left({p}\:,{q}\:\right)\:=\:\frac{\:\Gamma\:\left({p}\right)\Gamma\left({q}\right)}{\Gamma\left({p}+{q}\:\right)} \\ $$

Answered by MrGaster last updated on 28/Dec/24

Commented by mnjuly1970 last updated on 29/Dec/24

$$\:{thanks}\:{alot}\:{sir} \\ $$

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