By Milton Abramowitz, Irene A. Stegun

ISBN-10: 0486612724

ISBN-13: 9780486612720

Scholars and execs within the fields of arithmetic, physics, engineering, and economics will locate this reference paintings important. A vintage source for operating with exact features, common trig, and exponential logarithmic definitions and extensions, it positive factors 29 units of tables, a few to as excessive as 20 places.

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Extra info for Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics)

Sample text

Hence rprsrt fixes each of these four elements. By (iii) the claim follows. Thus if we put cp : p<—> rp then, by the above presentation, (R, cp) is a representation of IS. The last sentence in the statement of the proposition is rather clear. D In certain circumstances the geometry sUFifS,^ possesses some further automorphisms. , that G S R := R/Z(R). Let v : r — i > f be the natural homomorphism of R onto R. 2 (iii)) possesses a subgroup other than R which also acts regularly on the point-set of siS'^S, R).

Since the geometric triangles are contractible with respect to 8, (y) are adjacent in 0 , which means that the element a := q>(x)q>{y) belongs to the set (p(Tl) of generators. Since <5(a) = tp(z) we have a =

Furthermore, SC\R = Z(R), [R,S] = 1 and RS = H. This shows that H is the central product of R and S. 3)). In particular the automorphism of H which swaps the two central product factors R and S is an automorphism of sUFifS, R) and we obtain the following. 2) suppose that G S R : = R/Z(R). 2 (the central product of two copies of R extended by the automorphism which swaps the central factors) is an automorphism group ). 4) occurs when ^ is isomorphic to or

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Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics) by Milton Abramowitz, Irene A. Stegun


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