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hankel_2-powerseries-sin-taylor

powerseries(hankel_2(...

taylor(sin(z),z,0,3);

Calculate

hankel_2

hankel_2 (v,z);

Calculate

hankel_2-powerseries-sin-taylor

powerseries(hankel_2(...

taylor(sin(z),z,0,3);

Calculate

hankel_2-powerseries-sin-taylor

powerseries(hankel_2(...

taylor(sin(z),z,0,3);

Calculate

hankel_2-powerseries-sin-taylor

powerseries(hankel_2(...

taylor(sin(z),z,0,3);

Calculate

hankel_2

hankel_2 (v,z);

Calculate

hankel_2-powerseries

powerseries(hankel_2 ...

Calculate

hankel_2

hankel_2 (v,z);

Calculate

hankel_2

Run Example
(%i1)powerseries(hankel_2(1,z),z,0);
(%o1)                          Unable to expand
(%i2) powerseries(sin(z),z,0);
                           inf
                           ====        i2  2 i2 + 1
                           \      (- 1)   z
(%o2)                       >     -----------------
                           /         (2 i2 + 1)!
                           ====
                           i2 = 0
(%i3) 
Run Example
bessel_j(2/3,0.5);
(%o1)                          0.42331075068448
(%i2) bessel_y(2/3,0.5);
(%o2)                         - 1.131606010103143
(%i3) hankel_1(2/3,0.5);
(%o3)               0.42331075068448 - 1.131606010103144 %i
(%i4) hankel_2(2/3,0.5);
(%o4)               1.131606010103144 %i + 0.42331075068448
(%i5) bessel_j(0.4+%i*0.5,0.5);
(%o5)               0.55292006381987 - 0.43578387083041 %i
(%i6) bessel_j(0.4+%i*0.5,0.5+%i*2/3);
(%o6)               0.55449073054937 - 0.096849762699223 %i
(%i7) 
Run Example
bessel_j(2/3,0.5);
(%o1)                          0.42331075068448
(%i2) bessel_y(2/3,0.5);
(%o2)                         - 1.131606010103143
(%i3) hankel_1(2/5,0.5);
(%o3)               0.61880176080535 - 0.90269103008818 %i
(%i4) hankel_2(2/5,0.5);
(%o4)               0.90269103008818 %i + 0.61880176080535
(%i5) hankel_1(0.3+%i*0.5,0.5);
(%o5)                     hankel_1(0.5 %i + 0.3, 0.5)
(%i6) 

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