簡單搞個積

2023-03-23 21:00 作者:艾琳娜的糖果屋 0人讀過 | 我要投稿

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這里是個超幾何函數(shù)的積分，實際上我們可以考慮一般點的情況

考慮2F1的梅林變換

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這個結(jié)果利用2F1的積分表達(dá)或者拉馬努金主定理就能得到

其次是梅林變換的卷積定理 $%0A%5Cint_0%5E%7B%5Cinfty%7D%7Bx%5E%7Bs-1%7Df%5Cleft(%20x%20%5Cright)%20g%5Cleft(%20x%20%5Cright)%20%5Cmathrm%7Bd%7Dx%7D%3D%5Cfrac%7B1%7D%7B2%5Cpi%20i%7D%5Cint_%7Bc-i%5Cinfty%7D%5E%7Bc%2Bi%5Cinfty%7D%7BF%5Cleft(%20%5Cmu%20%5Cright)%20G%5Cleft(%20s-%5Cmu%20%5Cright)%20%5Cmathrm%7Bd%7D%5Cmu%7D%0A$

那么有

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再取s=c

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這里需要a-b不是整數(shù)，再帶入數(shù)據(jù)我們就能得到

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艾琳娜的糖果屋
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