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| f
| Taylor expansion,
f(c+x) = f(c) + (f'(c)/1!).x + (f''(c)/2!).x2
+ (f'''(c)/3!).x3 + ...
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|---|
| 1 / (1+x)r
| 1 - r x
+ r.(r+1)/2! x2
- r.(r+1).(r+2)/3! x3
+ ...
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| 1 / (1 - x)r
| 1 + r x + r.(r+1)/2! x2 + ...
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| log(1+x)
| x - 1/2 x2 + 1/3 x3 - ...
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| log(1 - x)
| - x - 1/2 x2 - 1/3 x3 - ...
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| sin x
| x - x3/3! + x5/5! - x7/7! + ...
|
| cos x
| 1 - x2/2! + x4/4! - x6/6! + ...
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| f(x) | d/dx f(x) |
| xn | n.xn-1 |
| log x | 1/x |
| x-n | -n.x-n-1 |
| ex | ex |
| xx | xx(ln(x) + 1) |
| sin x | cos x |
| cos x | - sin x |
| f(x)
| indefinite ∫ f(x) dx
| -∞∫+∞ f(x) dx
|
| xn | (1/(n+1)).xn+1 | |
| x-1 | log x | |
| 1 / (a+x2)k
|
x
.{hg([1/2,k], [3/2], -x2/a)}
/ ak
|
√π.Γ(k - 1/2)
/ {a(k-1/2).Γk}
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| x2 / (a+x2)k
| ?
|
√π.Γ(k - 3/2)
/ {2.a(k-3/2).Γk}
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| | meaning |
|---|
| hg() | hypergeometric() |
| Γ |
Γ function;
for int n, Γn=(n-1)! |
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