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1: Browsers
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►Although we have attempted to follow standards and maintain backwards compatibility with older browsers, you will generally get the best results by upgrading to the latest version of your preferred browser.
2: 21.1 Special Notation
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positive integers. | |
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intersection index of and , two cycles lying on a closed surface. if and do not intersect. Otherwise gets an additive contribution from every intersection point. This contribution is if the basis of the tangent vectors of the and cycles (§21.7(i)) at the point of intersection is positively oriented; otherwise it is . | |
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3: Guide to Searching the DLMF
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►Be careful, however, because if you put quotes around math expressions involving math symbols, you may not get the matches you’d expect.
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4: 4.10 Integrals
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4.10.5
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4.10.6
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►The left-hand side of (4.10.7) is a Cauchy principal value (§1.4(v)).
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►For ,
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4.10.10
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5: Wadim Zudilin
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►Robinson Award of the Canadian Mathematical Society.
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6: 19.22 Quadratic Transformations
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►Let , , , and .
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►If , then (19.22.7) reduces to (19.22.3), but if or , then both sides of (19.22.4) are 0 by (19.20.9).
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►(If , then and (19.22.13) reduces to (19.22.11).)
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►If or , then (19.22.20) reduces to by (19.20.13), and if or then (19.22.19) reduces to by (19.20.20) and (19.22.22).
…However, if and are complex conjugates and and are real, then the right-hand sides of all transformations in §§19.22(i) and 19.22(iii)—except (19.22.3) and (19.22.22)—are free of complex numbers and .
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7: 1.11 Zeros of Polynomials
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►Add to the roots of to get those of .
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8: 19.25 Relations to Other Functions
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►All terms on the right-hand sides are nonnegative when , , or , respectively.
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►The transformations in §19.7(ii) result from the symmetry and homogeneity of functions on the right-hand sides of (19.25.5), (19.25.7), and (19.25.14).
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►Let .
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►The sign on the right-hand side of (19.25.35) will change whenever one crosses a curve on which , for some .
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►The sign on the right-hand side of (19.25.40) will change whenever one crosses a curve on which , for some .
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9: Bibliography B
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Pi and the AGM, A Study in Analytic Number Theory and Computational Complexity.
Canadian Mathematical Society Series of Monographs and
Advanced Texts, John Wiley & Sons Inc., New York.
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