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1: 19.34 Mutual Inductance of Coaxial Circles
§19.34 Mutual Inductance of Coaxial Circles
The mutual inductance M of two coaxial circles of radius a and b with centers at a distance h apart is given in cgs units by
19.34.1 c 2 M 2 π = a b 0 2 π ( h 2 + a 2 + b 2 2 a b cos θ ) 1 / 2 cos θ d θ = 2 a b 1 1 t d t ( 1 + t ) ( 1 t ) ( a 3 2 a b t ) = 2 a b I ( 𝐞 5 ) ,
is the square of the maximum (upper signs) or minimum (lower signs) distance between the circles. … References for other inductance problems solvable in terms of elliptic integrals are given in Grover (1946, pp. 8 and 283).
2: 20 Theta Functions
Chapter 20 Theta Functions
3: Bibliography G
  • W. Gautschi (1994) Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software 20 (1), pp. 21–62.
  • A. Gil, J. Segura, and N. M. Temme (2014) Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
  • Ya. I. Granovskiĭ, I. M. Lutzenko, and A. S. Zhedanov (1992) Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.
  • K. I. Gross and D. St. P. Richards (1987) Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions. Trans. Amer. Math. Soc. 301 (2), pp. 781–811.
  • F. W. Grover (1946) Inductance Calculations. Van Nostrand, New York.
  • 4: Tom M. Apostol
    Apostol was born on August 20, 1923. … Tom Apostol and his wife Jane were inducted into the MAA’s Icosahedron Society in 2010. …
    5: 8 Incomplete Gamma and Related
    Functions
    6: 28 Mathieu Functions and Hill’s Equation
    7: 8.26 Tables
  • Khamis (1965) tabulates P ( a , x ) for a = 0.05 ( .05 ) 10 ( .1 ) 20 ( .25 ) 70 , 0.0001 x 250 to 10D.

  • Abramowitz and Stegun (1964, pp. 245–248) tabulates E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x = 0 ( .01 ) 2 to 7D; also ( x + n ) e x E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x 1 = 0 ( .01 ) 0.1 ( .05 ) 0.5 to 6S.

  • Pagurova (1961) tabulates E n ( x ) for n = 0 ( 1 ) 20 , x = 0 ( .01 ) 2 ( .1 ) 10 to 4-9S; e x E n ( x ) for n = 2 ( 1 ) 10 , x = 10 ( .1 ) 20 to 7D; e x E p ( x ) for p = 0 ( .1 ) 1 , x = 0.01 ( .01 ) 7 ( .05 ) 12 ( .1 ) 20 to 7S or 7D.

  • Zhang and Jin (1996, Table 19.1) tabulates E n ( x ) for n = 1 , 2 , 3 , 5 , 10 , 15 , 20 , x = 0 ( .1 ) 1 , 1.5 , 2 , 3 , 5 , 10 , 20 , 30 , 50 , 100 to 7D or 8S.

  • 8: 23 Weierstrass Elliptic and Modular
    Functions
    9: 36 Integrals with Coalescing Saddles
    10: Gergő Nemes
    As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …