Mathematics-I (3110014)

$\mathrm{We} \mathrm{know} \mathrm{that}, \mathrm{\beta }(\mathrm{m},\mathrm{n})=\frac{\lceil \mathrm{m} \lceil \mathrm{n}}{\lceil \left(\mathrm{m}+\mathrm{n}\right)}$

$\mathrm{\beta }\left(\frac{7}{2},\frac{5}{2}\right)=\frac{\lceil \left(\frac{7}{2}\right) \lceil \left(\frac{5}{2}\right)}{\lceil \left(\frac{7}{2}+\frac{5}{2}\right)}$

$\mathrm{\beta }\left(\frac{7}{2},\frac{5}{2}\right)=\frac{\frac{5}{2}·\frac{3}{2}·\frac{1}{2}·\sqrt{\mathrm{\pi }}·\frac{3}{2}·\frac{1}{2}·\sqrt{\mathrm{\pi }}}{\lceil 6} [ \lceil \mathrm{n}=(\mathrm{n}-1)\lceil (\mathrm{n}-1) ]$

$\mathrm{\beta }\left(\frac{7}{2},\frac{5}{2}\right)=\frac{45·\mathrm{\pi }}{32·5·4·3·2·1}$

$\mathrm{\beta }\left(\frac{7}{2},\frac{5}{2}\right)=\frac{3\mathrm{\pi }}{256}$