Heine transformations (first, second, third)
(0.004 seconds)
1—10 of 516 matching pages
1: 1.14 Integral Transforms
§1.14 Integral Transforms
►§1.14(i) Fourier Transform
… ►§1.14(iii) Laplace Transform
… ►Fourier Transform
… ►Laplace Transform
…2: 14.28 Sums
3: 18.7 Interrelations and Limit Relations
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§18.7(i) Linear Transformations
… ►§18.7(ii) Quadratic Transformations
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18.7.17
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18.7.18
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► See §18.11(ii) for limit formulas of Mehler–Heine type.
4: Bibliography V
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A Fortran computer program for calculating the oblate spheroidal radial functions of the first and second kind and their first derivatives.
NRL Report No. 6959
Naval Res. Lab. Washingtion, D.C..
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Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives.
Quart. Appl. Math. 62 (3), pp. 493–507.
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On the series expansion method for computing incomplete elliptic integrals of the first and second kinds.
Math. Comp. 23 (105), pp. 61–69.
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Transformations of some Gauss hypergeometric functions.
J. Comput. Appl. Math. 178 (1-2), pp. 473–487.
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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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5: 17.6 Function
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Heine’s First Transformation
… ►Heine’s Second Tranformation
… ►Heine’s Third Transformation
… ►Fine’s First Transformation
… ►Heine’s Contiguous Relations
…6: 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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►Abramowitz and Stegun (1964): , , , , for , , , , respectively, when .
►Jeffreys and Jeffreys (1956): for , for , for .
►Whittaker and Watson (1927): for .
►For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).
7: 14.12 Integral Representations
8: 18.11 Relations to Other Functions
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18.11.1
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►For the Ferrers function , see §14.3(i).
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§18.11(ii) Formulas of Mehler–Heine Type
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18.11.5
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18.11.6
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9: 19.7 Connection Formulas
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