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- Almkvist, Gert, et al.
(författare)
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Apery Limits of Differential Equations of Order 4 and 5
- 2008
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Ingår i: MODULAR FORMS AND STRING DUALITY. ; 54, s. 105-123
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Konferensbidrag (refereegranskat)abstract
- The concept of Apery limit for second and third order differential equations is extended to fourth and fifth order equations, mainly of Calabi-Yau type. For those equations obtained from Hadamard products of second and third order equations we can prove that the limits are determined in terms of the factors by a certain formula. Otherwise the limits are found by using PSLQ in Maple and are only conjectural. All identified limits are rational linear combinations of the following numbers: pi(2) Catalan's constant G, Sigma(infinity)(n=1) (n/3)/n(2); pi(3), pi(3), zeta(3), pi(3)root 3, pi(4).
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| 4. |
- Almkvist, Gert, et al.
(författare)
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Polynomials a' la Lehmers and Wilf
- 2009
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Ingår i: Mathematical Reports of the Academy of Science. - 0706-1994. ; 31:3, s. 65-71
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Almkvist, Gert, et al.
(författare)
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Some new formulas for pi
- 2003
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Ingår i: Experimental Mathematics. - 1944-950X. ; 12:4, s. 441-456
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Tidskriftsartikel (refereegranskat)abstract
- We show how to find series expansions for pi of the form pi = Sigma(n=0)(infinity) S(n)/((mn)(pn)) a(n), is some polynomial in n (depending on m,p,a). We prove that there exist such expansions for m = 8k, p = 4k, a = (-4)(k), for any k, and give explicit examples for such expansions for small values of m, p and a.
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