Rodrigue's formula, on the other hand, will invariably be introduced as a formula that enables you to generate Legendre polynomials of any order without recourse to the method of separation of variables.
Although liver biopsy remains the gold standard for disease assessment, the development of risk scores, biomarker panels and ultrasound modalities has resulted in much improved identification of at risk patients without recourse to use of liver biopsy on a routine basis.
If φ is a sentence of IFL not truth equivalent to any FO sentence, the truth-condition of the sentence ¬φ of EIFL cannot be formulated without recourse to the set of all strategies of player 2: ¬φ is true in model M iff for all strategies of player 2 in game G φ, M), there is a sequence of moves by player 1 such that player 1 wins the resulting play.
Geometric mechanics, which develops traditional geometric methods of mechanics, enables one to construct theories of complex coupled systems on the basis of Newtonian axiomatics without recourse to the methods of Lagrangian analytical mechanics, Euler's methods for the dynamics of a rigid body and other theories and principles.
It is a response to modern evolutionary theory, which explains the emergence and diversity of life without recourse to the doctrine of God or any other divine power.
Countless one-liners capture the essence of Oscar Wilde's The Importance of Being Earnest without recourse to an item of luggage (clue: 7 letters beginning with H).
The immediacy of the voice is enough to make you think about how such a scenario came about, without recourse to pages of exposition.
While the majority took advantage of the Saturday-morning kick-off to embark on a stunning bender, those of us who had failed to plan ahead and book the day off work had to watch it at home without recourse to pints of Fast-Acting Nerve Calmer.
The resulting numerical algorithm converges with high order accuracy without recourse to use of meshes finer than those resulting from the cosine transformation.
Strong representationalism (defended by Dretske, Tye and Lycan) is the view that representation of a certain kind suffices for a sensory quality, where the kind can be specified in functionalist or other familiar materialist terms, without recourse to properties of any ontologically "new" sort.
