applications to physics (see , ) and in geometric function theory (see , ). From antiquity several more easily computable approximations to L(a, b) have been suggested. The Almkvist–Berndt survey article  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 . An excellent source for all of the above ideas is the Anderson–Vamanamurthy–Vuorinen book Conformal Invariants, Inequalities, and Quasiconformal Mappings . In 1883, it was proposed by Muir (see ) 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 . This was announced at several international conferences. Letting x =1 − b2, he asked whether the Muir approximatio
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