Digital Library of Mathematical Functions
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18 Orthogonal PolynomialsClassical Orthogonal Polynomials

§18.4 Graphics

Contents

§18.4(i) Graphs

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Figure 18.4.1: Jacobi polynomials Pn(1.5,-0.5)(x), n=1,2,3,4,5. Magnify
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Figure 18.4.2: Jacobi polynomials Pn(1.25,0.75)(x), n=7,8. This illustrates inequalities for extrema of a Jacobi polynomial; see (18.14.16). See also Askey (1990). Magnify
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Figure 18.4.3: Chebyshev polynomials Tn(x), n=1,2,3,4,5. Magnify
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Figure 18.4.4: Legendre polynomials Pn(x), n=1,2,3,4,5. Magnify
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Figure 18.4.5: Laguerre polynomials Ln(x), n=1,2,3,4,5. Magnify
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Figure 18.4.6: Laguerre polynomials L3(α)(x), α=0,1,2,3,4. Magnify
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Figure 18.4.7: Monic Hermite polynomials hn(x)=2-nHn(x), n=1,2,3,4,5. Magnify

§18.4(ii) Surfaces

Figure 18.4.8: Laguerre polynomials L3(α)(x), 0α3, 0x10. Magnify
Figure 18.4.9: Laguerre polynomials L4(α)(x), 0α3, 0x10. Magnify