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| Whenever you have a fractional power, there is the possibility of extraneous complex roots. (6x-5)^(4/3) = 625 = 625 * 1 Taking the 3/4 th power and noting that 1^(3/4) = Exp[(3/2)n Pi I], n = 0, 1, 2 ... you get 6x-5 = 125 Exp[(3/2)n Pi I] ... |
| Programs producing Bezier functions, etc. do not generally show the functional form of the interpolated curve. They usually involve what are called Bernstein polynomials. You might be able to work out the functions after reading... |
| Example with 2x2 orthogonal matrix In[2]:= A = {{Cos[\[Theta]], -Sin[\[Theta]]}, {Sin[\[Theta]], Cos[\[Theta]]}}; In[3]:= AT = Transpose[A]; In[4]:= Simplify[A.AT] Out[4]= {{1, 0}, {0, 1}} Now, in... |
| Try FullSimplify[...] on both forms. You get almost identical results. |
| Several syntax errors. N is a reserved symbol for numerical value. A and B should be defined as functions A[k_]:= , etc. [ ] cannot be used as grouping brackets; use ( ). [ ] reserved for function definitions. Here is corrected sample of part of... |
| You can simulate quaternions with a linear combination of the 3 Pauli spin matrices and the 2x2 identity matrix. |
| To convert an expression to AMS LaTeX form use TeXForm[expr]. Look up LaTeX in Wolfram Documentation for further details. |
| Break up the evaluation as follows: In[15]:= Integrate[ HypergeometricU[1, 1, z k] k^(a - 1) (1 - k)^(-a), {k, 0, 1}] Out[15]= ConditionalExpression[\[Pi] Csc[a \[Pi]] Gamma[ a] HypergeometricU[a, 1, z], 0 |
| More directly, something like In[9]:= f[i_, j_, \[Theta]_] := R[i, j] Cos[\[Theta]] Sign[j - i] In[10]:= f[1, 2, \[Theta]] Out[10]= Cos[\[Theta]] R[1, 2] In[11]:= f[2, 1, \[Theta]] Out[11]=... |
| For some identities involving 3F2, see http://functions.wolfram.com/HypergeometricFunctions/Hypergeometric3F2/ |