Question
Answer some questions about fractional calculus, which studies derivatives of fractional orders. For 10 points each:
[10e] The power rule of normal calculus can be generalized for fractional order by replacing this function in the coefficient by the gamma function. This function of n is the product of all positive integers smaller or equal to n.
ANSWER: factorial
[10m] The half derivative of x is equal to 2 times the square root of x divided by the square root of this number. The Riemann zeta of 2 is equal to this number squared over 6.
ANSWER: pi
[10h] The half derivative of the exponential function contains a term that is proportional to e to the x times this function of the square root of x. Defined as the integral of the Gaussian exponential, this function is proportional to the area under the normal distribution.
ANSWER: error function [or erf]
<Leo Law, Other Science>
Summary
| 2023 Penn Bowl @ Waterloo | 10/28/2023 | Y | 2 | 30.00 | 100% | 100% | 100% |
| 2023 Penn Bowl (Harvard) | 10/21/2023 | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2023 Penn Bowl (Mainsite) | 10/21/2023 | Y | 5 | 22.00 | 100% | 100% | 20% |
| 2023 Penn Bowl (Norcal) | 10/28/2023 | Y | 1 | 30.00 | 100% | 100% | 100% |
| 2023 Penn Bowl (UK) | 10/28/2023 | Y | 5 | 22.00 | 100% | 80% | 40% |
Data
| Stanford | Berkeley A | 10 | 10 | 10 | 30 |