contiguous relations
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9 matching pages
1: 16.4 Argument Unity
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►The characterizing properties (18.22.2), (18.22.10), (18.22.19), (18.22.20), and (18.26.14) of the Hahn and Wilson class polynomials are examples of the contiguous relations mentioned in the previous three paragraphs.
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►See Bailey (1964, §§4.3(7) and 7.6(1)) for the transformation formulas and Wilson (1978) for contiguous relations.
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2: 15.5 Derivatives and Contiguous Functions
3: 18.9 Recurrence Relations and Derivatives
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§18.9(ii) Contiguous Relations in the Parameters and the Degree
…4: 17.6 Function
5: 18.2 General Orthogonal Polynomials
6: Bibliography G
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Contiguous relations and summation and transformation formulae for basic hypergeometric series.
J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
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7: 16.3 Derivatives and Contiguous Functions
8: Bibliography S
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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations.
SIAM J. Math. Anal. 10 (4), pp. 823–838.
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Chebyshev expansions for the error and related functions.
Math. Comp. 32 (144), pp. 1232–1240.
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Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros.
Math. Comp. 70 (235), pp. 1205–1220.
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Interlacing of the zeros of contiguous hypergeometric functions.
Numer. Algorithms 49 (1-4), pp. 387–407.
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Structure of avoided crossings for eigenvalues related to equations of Heun’s class.
J. Phys. A 30 (2), pp. 673–687.
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9: 10.21 Zeros
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►The positive zeros of any two real distinct cylinder functions of the same order are interlaced, as are the positive zeros of any real cylinder function and the contiguous function .
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►The functions and are related to the inverses of the phase functions and defined in §10.18(i): if , then
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