## Methods of summation |

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### Contents

THE DIFFERENCE OPERATOR A DIFFERENCES | 1 |

THE OPERATORS Al AND I | 11 |

REPEATED DIFFERENCES DIFFERENCES | 20 |

Copyright | |

9 other sections not shown

### Common terms and phrases

additive constant applied arbitrary order asymptotic formula Bernoulli numbers Bernoulli polynomials binomial coefficients companion series Compute cos(ax decomposed into partial defined differentiation duplication formula equal equation equivalent difference Estimate the sum Euler-Maclaurin formula Euler's constant evaluate Example III-5 Example V-12 Exercises Section Find the antidifference Find the sum formula 16 Fourier series Fractional Calculus functional relations fundamental theorem gamma function geometric series given gives identify ux indeterminate form oo infinite series interval Laplace transform ln(l ln(t lnT(r method multiplied nth factorial functions original series partial fraction decomposition problem psi function r=l r=l rapidity of convergence rate of convergence recurrence formula reflection formula replaced result right side Section VIII series expansion series whose sum Show sin(ax sinh substituted sum calculus sum of nth sum of reciprocal summation of series summation sign Table II-1 tetragamma functions transformed series upper limit values Verify write yields zero