modified functions
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11: 10.76 Approximations
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§10.76(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions
… ►Real Variable; Imaginary Order
…12: 11.3 Graphics
13: 10.66 Expansions in Series of Bessel Functions
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10.66.1
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14: 11.1 Special Notation
§11.1 Special Notation
… ►For the functions , , , , , and see §§10.2(ii), 10.25(ii). ►The functions treated in this chapter are the Struve functions and , the modified Struve functions and , the Lommel functions and , the Anger function , the Weber function , and the associated Anger–Weber function .15: 10.74 Methods of Computation
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►In the case of the modified Bessel function
see especially Temme (1975).
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Kontorovich–Lebedev Transform
… ►§10.74(viii) Functions of Imaginary Order
…16: 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
, , , .
For the spherical Bessel functions and modified spherical Bessel functions the order is a nonnegative integer.
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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).
17: 11.2 Definitions
§11.2 Definitions
►§11.2(i) Power-Series Expansions
… ► … ►Particular solutions: … ►Particular solutions: …18: 10.28 Wronskians and Cross-Products
19: 28.22 Connection Formulas
§28.22 Connection Formulas
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28.22.3
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►The joining factors in the above formulas are given by
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28.22.13
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20: 10.73 Physical Applications
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