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 $\normal B_{x}(a,b)={\large\int_{\small 0}^{\hspace{25}x}}t^{a-1}(1-t)^{b-1}dt\\[10]$
 ϕ֐: f(t,a,b)= ϐ a , b ϕ( , x ) [ n 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ]
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 $\normal Incomplete\ beta\ functions\ B_x(a,b),\ I_x(a,b)\\[10](1)\ Incomplete\ beta\ function\\\hspace{40}B_{x}(a,b)={\large\int_{\small 0}^{\hspace{25}x}}t^{a-1}(1-t)^{b-1}dt\\[10](2)\ Regularized\ incomplete\ beta\ function\\\hspace{40}I_{x}(a,b)={\large\frac{B_{x}(a,b)}{B(a,b)}}\\[10](3)\ Complete\ beta\ function\\\hspace{40}B(a,b)={\large\int_{\small 0}^{\hspace{25}\small 1}}t^{a-1}(1-t)^{b-1}dt\\$

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