Euler—Maclaurin Summation Formula
Problems

3 Series Involving Zeta Functions
3．1 Historicallntroduction
3．2 Use of the Binomial Theorem
Applications of Theorems 3．1 and 3．2
3．3 Use of Generating Functions
Series Involving Polygamma Functions
Series Involving Polylogarithm Functions
3．4 Use of Multiple Gamma Functions
Evaluation by Using the Gamma Function
Evaluation in Terms of Catalan's Constant G
Further Evaluation by Using the Triple Gamma Function
Applications of Corollary 3．3
3．5 Use of Hypergeometric Identities
Series Derivable from Gauss's Summation Formula 1．4（7）
Series Derivable from Kummer's Formula （3）
Series Derivable from Other Hypergeometric Summation Formulas
Further Summation Formulas Related to Generalized Harmonic Numbers
3．6 Other Methods and their Applications
The Weierstrass Canonical Product Form for the Gamma Function
Evaluation by Using Infinite Products
Higher—Order Derivatives of the Gamma Function
3．7 Applications of Series Involving the Zeta Function
The Multiple Gamma Functions
Mathieu Series
Problems

4 Evaluations and Series Representations
4．1 Evaluation of ζ（2n）
The General Case of ζ（2n）
4．2 Rapidly Convergent Series for ζ（2n + 1）
Remarks and Observations
4．3 Further Series Representations
4．4 ComputationaIResults
Problems

5 Determinants of the Laplacians
5．1 The n—Dimensional Problem
5．2 Computations Using the Simple and Multiple Gamma Functions
Factorizations Into Simple and Multiple Gamma Functions
Evaluations of det'△n （n=1， 2， 3）
5．3 Computations Using Series of Zeta Functions
5．4 Computations using Zeta Regularized Products
A Lemma on Zeta Regularized Products and a Main Theorem
Computations for small n
5．5 Remarks and Observations
Problems

6 q—Extensions of Some Special Functions and Polynomials
6．1 q—Shifted Factorials and q—Binormal Coefficients
6．2 q—Derivative， q—Antiderivative and Jackson q—lntegral
q—Derivative
q—Antiderivative and Jackson q—lntegral
6．3 q—Binomial Theorem
6．4 q—Gamma Function and q—Beta Function
q—Gamma Function
q—Beta Function
6．5 A q—Extension of the Multiple Gamma Functions
6．6 q—Bernoulli Numbers and q—Bernoulli Polynomials
q—Stirling Numbers of the Second Kind
The Polynomial βk（x）=βk；q（X）
6．7 q—Euler Numbers and q—Euler Polynomials
6．8 The q—Apostol—Bernoulli Polynomials βk（n） （x；λ） of Order n
6．9 The q—Apostol—Euler Polynomials εEk（n）（x；λ） of Order n
6．10 A Generalized q—Zeta Function
An Auxiliary Function Defining Generalized q—Zeta Function
Application of Euler—Maclaurin Summation Formula
6．11 Multiple q—Zeta Functions
Analytic Continuation of gq and ζq
Analytic Continuation of Multiple Zeta Functions
Special Values of ζq （s1， s2）
Problems

7 Miscellaneous Results
7．1 A Set of Useful Mathematical Constants
Euler—Mascheroni Constant γ
Series Representations for γ
A Class of Constants Analogous to {Dk}
Other Classes of Mathematical Constants
7．2 Log—Sine Integrals Involving Series Associated with the Zeta Function and Polylogarithms
Analogous Log—Sine Integrals
Remarks on Cln （θ） and Gln （θ）
Further Remarks and Observations
7．3 Applications of the Gamma and Polygamma Functions Involving
Convolutions of the Rayleigh Functions
Series Expressible in Terms of the ψ—Function
Convolutions of the Rayleigh Functions
7．4 Bernoulli and Euler Polynomials at Rational Arguments
The Cvijovie—Klinowski Summation Formulas
Srivastava's Shorter Proofs of Theorem 7．3 and Theorem 7．4
Formulas Involving the Hurwitz—Lerch Zeta Function
An Application of Lerch's Functional Equation 2．5（29）
7．5 Closed—Form Summation of Trigonometric Series
Problems

Bibliography
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