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By R. W. Barnard, K. Pearce and K. C. Richards


applications to physics (see [11], [9]) and in geometric function theory (see [10], [3]). From antiquity several more easily computable approximations to L(a, b) have been suggested. The Almkvist–Berndt survey article [2] has an extensive discussion of these approximations. These approximations and their historical and recent connections to the approximations of π can be found in the Borweins ’ book [6]. An excellent source for all of the above ideas is the Anderson–Vamanamurthy–Vuorinen book Conformal Invariants, Inequalities, and Quasiconformal Mappings [3]. In 1883, it was proposed by Muir (see [2]) that L(1,b) could be simply approximated by 2π[(1 + b3/2)/2] 2/3. A close numerical examination of the error in this approximation lead M. Vuorinen to pose Problem 5.6 in [13]. This was announced at several international conferences. Letting x =1 − b2, he asked whether the Muir approximatio

Topics: F (−n, c − a, b, c
Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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