Functions of a Complex VariableGinn, 1914 - 583 páginas A thorough treatment of fundamental elements, concepts, and theorems pertaining to the function of a complex variable, this rigorous treatment is suitable for advanced mathematics students, physicists, and engineers. 1914 edition. |
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Otras ediciones - Ver todo
Términos y frases comunes
a₁ a₂ absolutely convergent addition theorem algebraic function an+1 analytic function b₁ b₂ branch points C₁ C₂ calculus called circle of convergence closed curve coefficients complex numbers connex constant continuous function convergent series converges absolutely converges steadily corresponding cosh defined denote differential divergent domain of definition elliptic functions equation essentially singular point Example expressed finite gives Hence infinite product infinite series integral interval Let us set Let us show limit logarithmic one-valued analytic function one-valued function period plane point set pole of order positive term series power series quotient radius rational functions reader real numbers rectangles relation roots Similarly sin² sinh sn² Suppose symbol transcendental function vanish variable w₁ w₂ whole z-plane z-plane zeros α₁ πί ди дх მყ
Pasajes populares
Página 12 - Thus, the modulus of the quotient is the quotient of the moduli and the argument of the quotient is obtained by subtracting the argument of the denominator from that of the numerator...
Página 522 - Hence the required formulas are x = r sin в cos ф, у = r sin в sin ф, z =r cos в.
Página 255 - A polynomial in .x and y is the sum of a finite number of terms of the type...
Página 517 - In the case of the sphere these are x = r sin 6 cos $ , y = r sin 0 sin <f> , z = r cos 0.
Página 494 - ... x = r sin 6 cos <f>, y — r sin 6 sin <f>, z = r cos 6.
Página 53 - ~TTF+' 1.2.8 ' and 5 therefore diverges in this case. To sum up, we have the theorem : The binomial series 1) converges absolutely for x < 1, and diverges for \x\ > 1. When x= 1, it converges for p > — 1 and diverges for fj, < — 1 ; it converges absolutely only for fj,> 0.
Página 469 - The only singular point in the finite part of the plane is x = 0. Let us consider the integrals of 1) for this point. The equation is already in the normal form. Here The indicial equation for x = 0 is therefore /0(r)= - w2 + r + r(r- 1)= 0, /0(r)=»*-ro
Referencias a este libro
Wide-tuning Range S-band Traveling-wave Maser Stanford University. Stanford Electronics Laboratories,John C. Cromack No hay ninguna vista previa disponible - 1963 |