TY - JOUR
AU - Wilson, B. M.
AB - PSEUDO-ORTHOGONAL SYSTEMS OF FUNCTIONS. 59 ON PSEUDO-ORTHOGONAL SYSTEMS OF FUNCTIONS ARISING AS SOLUTIONS OF AN INTEGRAL EQUATION By B. M. WILSON. [Received 26 February, 1924.—Read 13 March, 1924. Received in revised form 27 January, 1925.] 1. IN a paper recently presented to the London Mathematical Society, Prof. Proudman has discussed the representation of an "arbitrary" function by a series of the type I,A v (x), where the functions v(x) are n n denned by means of the differential equation Xv{x) = 1 (0 1) j + ~ < *'< together with the boundary conditions (1 . 2) ©'(0) = ©(1) = 0, and the characteristic constants of the problem, ^•1 , ^-2, A3 , ..., are determined by the condition that (1.8) v f ©«(x) ( dx — a\ , n n J Jo o where a is a given real constant.* From equations (1.1), (1.2), and (1.3 ) it readily follows that (1.4) 1 v (x) v (x) dx = a (m =£ n). m n )o * J. Proudman, Proc. London Math. Soc. (2), 24 (1925), 131-139. I wish to express my thanks to Prof. Proudman for allowing me to read his paper while still in manuscript. 
TI - On Pseudo‐Orthogonal Systems of Functions Arising as Solutions of an Integral Equation
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s2-25.1.59
DA - 1926-01-01
UR - https://www.deepdyve.com/lp/wiley/on-pseudo-orthogonal-systems-of-functions-arising-as-solutions-of-an-Sl70CFp8Qd
SP - 59
EP - 102
VL - s2-25
IS - 1
DP - DeepDyve
ER -