The laminar boundary layer in axial flow along a long thin cylinder with constant temperature is investigated by expanding in powers of a variable ξ that was used by Seban & Bond [J. Aero. Sci., 18 (1951), 671.]. The series solutions for the skin friction, the local Nusselt number and the other boundary-layer parameters are obtained up to about 20 terms, and by utilizing Pade approximants, their singular points on a complex plane are evaluated. Euler transformations then yield more convergent expansions, and by reflecting the known asymptotic behavior of the solutions on the extended series solutions, reasonable solutions are obtained for sufficiently large ξ. It is clarified that the solutions by the method of analytic continuation using Pade approximants are also reasonable. Pade approximants are applied further to velocity and temperature distributions.