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1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

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1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

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Mathematics · 术语表

什么是 Asymptotic expansion？

Definition 6.2 University Mathematics — Year 2 · 第 6 章 — Comparison of Functions

$f$ admits the asymptotic expansion

f = c_1 \varphi_1 + c_2\varphi_2 + \dots + c_k \varphi_k + o(\varphi_k) \qquad (\varphi_{i+1} = o(\varphi_i) \text{ in the scale})

when the successive remainders satisfy the displayed estimates. The coefficients are then unique: $c_1 = \lim f/\varphi_1$ , and inductively $c_{i+1} = \lim\,(f - \sum_{j \leq i} c_j\varphi_j)/\varphi_{i+1}$ .

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