for Bessel and Hankel functions
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1: 10.1 Special Notation
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►The main functions treated in this chapter are the Bessel functions
, ; Hankel functions
, ; modified Bessel functions
, ; spherical Bessel functions
, , , ; modified spherical Bessel functions
, , ; Kelvin functions
, , , .
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►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
2: 10.76 Approximations
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§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
…3: 10.4 Connection Formulas
4: 10.5 Wronskians and Cross-Products
5: 10.2 Definitions
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§10.2(i) Bessel’s Equation
… ►Bessel Functions of the Third Kind (Hankel Functions)
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10.2.5
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Branch Conventions
►Except where indicated otherwise, it is assumed throughout the DLMF that the symbols , , , and denote the principal values of these functions. …6: 10.11 Analytic Continuation
7: 10.3 Graphics
§10.3 Graphics
►§10.3(i) Real Order and Variable
►For the modulus and phase functions , , , and see §10.18. … ►§10.3(ii) Real Order, Complex Variable
… ►§10.3(iii) Imaginary Order, Real Variable
…8: 10.74 Methods of Computation
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►The power-series expansions given in §§10.2 and 10.8, together with the connection formulas of §10.4, can be used to compute the Bessel and Hankel functions when the argument or is sufficiently small in absolute value.
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►For the function
, for example, can always be computed in a stable manner in the sector by integrating along rays towards the origin.
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►For evaluation of the Hankel functions
and for complex values of and based on the integral representations (10.9.18) see Remenets (1973).
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