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From Ck=[{e^(-Scl)*gamma(N+1)*gamma(N+1+u)}/{gamma(1+u)}]/[{gamma(N+1+a-k)*gamma(N+1+b-k)}/{gamma(1+a-k)*gamma(1+b-k)}]

How to prove Ck=[e^(-Scl)*{gamma(1+a-k)*gamma(1+b-k)}]/{gamma(1+u)}

to get Ck=[{gamma(1+a)*gamma(1+b)}/{gamma^2(1+k)*gamma(1+u)}]*e^(Scl)?

by u=[g*Beta*Ec]/[2*(pi)^2]

where the correction of order 1/N may be ignored. Employing the definition of the gamma function ; gamma(N+1+a)=(N+a)(N+a-1)...(1+a)a!

How to prove Ck=[e^(-Scl)*{gamma(1+a-k)*gamma(1+b-k)}]/{gamma(1+u)}

to get Ck=[{gamma(1+a)*gamma(1+b)}/{gamma^2(1+k)*gamma(1+u)}]*e^(Scl)?

by u=[g*Beta*Ec]/[2*(pi)^2]

where the correction of order 1/N may be ignored. Employing the definition of the gamma function ; gamma(N+1+a)=(N+a)(N+a-1)...(1+a)a!

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