Lagrange%20inversion%20theorem
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1: 4.37 Inverse Hyperbolic Functions
§4.37 Inverse Hyperbolic Functions
… ►Inverse Hyperbolic Sine
… ►Inverse Hyperbolic Cosine
… ►Inverse Hyperbolic Tangent
… ►Other Inverse Functions
…2: 4.23 Inverse Trigonometric Functions
§4.23 Inverse Trigonometric Functions
… ►Inverse Sine
… ►Inverse Cosine
… ►Inverse Tangent
… ►Other Inverse Functions
…3: 22.15 Inverse Functions
§22.15 Inverse Functions
►§22.15(i) Definitions
… ►Each of these inverse functions is multivalued. The principal values satisfy … ►4: 18.40 Methods of Computation
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Stieltjes Inversion via (approximate) Analytic Continuation
… ►Results of low ( to decimal digits) precision for are easily obtained for to . … ►Histogram Approach
… ►In what follows this is accomplished in two ways: i) via the Lagrange interpolation of §3.3(i) ; and ii) by constructing a pointwise continued fraction, or PWCF, as follows: … ►Comparisons of the precisions of Lagrange and PWCF interpolations to obtain the derivatives, are shown in Figure 18.40.2. …5: 3.3 Interpolation
§3.3 Interpolation
►§3.3(i) Lagrange Interpolation
… ► ►With an error term the Lagrange interpolation formula for is given by … ►§3.3(ii) Lagrange Interpolation with Equally-Spaced Nodes
…6: 20 Theta Functions
Chapter 20 Theta Functions
…7: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Oscillatory integrals, Lagrange immersions and unfolding of singularities.
Comm. Pure Appl. Math. 27, pp. 207–281.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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8: 3.4 Differentiation
9: 1.10 Functions of a Complex Variable
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Picard’s Theorem
… ►§1.10(iv) Residue Theorem
… ►§1.10(vii) Inverse Functions
►Lagrange Inversion Theorem
… ►Extended Inversion Theorem
…10: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Barycentric Lagrange interpolation.
SIAM Rev. 46 (3), pp. 501–517.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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