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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
1. Finite differences.
2. Gauss-Hermite Integration.
A. Gram-Schmidt orthogonalization.
B. Definition and existence of orthogonal polynomials.
C. Three-term recurrence relation for orthogonal polynomials.
D. Orthogonal polynomials and quadrature rules.
E. Extremal properties of orthogonal polynomials.
F. Chebyshev polynomials.
3. Asymptotic expansions.
4. Monte-Carlo.
5. Convex Analysis.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Extremal properties of orthogonal polynomials.


roposition

(Extremal properties of orthogonal polynomials) Let MATH be the orthogonal polynomials with respect to the measure $d\lambda$ . Then MATH

Proof

By the proposition ( Basic property of orthogonal polynomials ), for any MATH we have MATH for some numbers MATH . The leading term is such because MATH By orthogonality of MATH , MATH Thus MATH is achieved at $c_{k}=0,\forall k.$





Notation. Index. Contents.


















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