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1: 28.12 Definitions and Basic Properties
The introduction to the eigenvalues and the functions of general order proceeds as in §§28.2(i), 28.2(ii), and 28.2(iii), except that we now restrict ν ^ 0 , 1 ; equivalently ν n . …
§28.12(ii) Eigenfunctions me ν ( z , q )
For q = 0 , …
2: 28.2 Definitions and Basic Properties
§28.2(vi) Eigenfunctions
3: 34.11 Higher-Order 3 n j Symbols
§34.11 Higher-Order 3 n j Symbols
4: 10.24 Functions of Imaginary Order
§10.24 Functions of Imaginary Order
and J ~ ν ( x ) , Y ~ ν ( x ) are linearly independent solutions of (10.24.1): … In consequence of (10.24.6), when x is large J ~ ν ( x ) and Y ~ ν ( x ) comprise a numerically satisfactory pair of solutions of (10.24.1); compare §2.7(iv). … …
5: 10.45 Functions of Imaginary Order
§10.45 Functions of Imaginary Order
and I ~ ν ( x ) , K ~ ν ( x ) are real and linearly independent solutions of (10.45.1): … The corresponding result for K ~ ν ( x ) is given by …
6: 10.26 Graphics
§10.26(i) Real Order and Variable
§10.26(ii) Real Order, Complex Variable
§10.26(iii) Imaginary Order, Real Variable
See accompanying text
Figure 10.26.7: I ~ 1 / 2 ( x ) , K ~ 1 / 2 ( x ) , 0.01 x 3 . Magnify
See accompanying text
Figure 10.26.8: I ~ 1 ( x ) , K ~ 1 ( x ) , 0.01 x 3 . Magnify
7: 10.76 Approximations
Real Variable and Order : Functions
Real Variable and Order : Zeros
Real Variable and Order : Integrals
Complex Variable; Real Order
Real Variable; Imaginary Order
8: 10.77 Software
§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)
§10.77(iii) Bessel Functions–Real Order and Argument
§10.77(vi) Bessel Functions–Imaginary Order and Real Argument
§10.77(vii) Bessel Functions–Complex Order and Real Argument
§10.77(viii) Bessel Functions–Complex Order and Argument
9: 10.3 Graphics
§10.3(i) Real Order and Variable
§10.3(ii) Real Order, Complex Variable
§10.3(iii) Imaginary Order, Real Variable
See accompanying text
Figure 10.3.18: J ~ 1 ( x ) , Y ~ 1 ( x ) , 0.01 x 10 . Magnify
See accompanying text
Figure 10.3.19: J ~ 5 ( x ) , Y ~ 5 ( x ) , 0.01 x 10 . Magnify
10: 11.1 Special Notation
§11.1 Special Notation
x real variable.
ν real or complex order.
n integer order.