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RiemannSiegelZ






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelZ[z] > Series representations > Asymptotic series expansions





http://functions.wolfram.com/10.04.06.0011.01









  


  










Input Form





RiemannSiegelZ[z] \[Proportional] (Exp[-((I (4 z^2 + Pi Sqrt[z^2]))/(8 z))] (z^2)^((I z)/4) (1 + (3 I)/(16 z) - 9/(512 z^2) + (183 I)/(8192 z^3) - 2277/(524288 z^4) + (212829 I)/(8388608 z^5) - 1364445/(268435456 z^6) + (326341455 I)/(4294967296 z^7) - 8198081325/(549755813888 z^8) + (3781776345585 I)/(8796093022208 z^9) - 23339010744567/ (281474976710656 z^10) + (17654423117199729 I)/ (4503599627370496 z^11) - 215619469740469809/(288230376151711744 z^12) + (241858525676475612513 I)/(4611686018427387904 z^13) - 1468114834103562061701/(147573952589676412928 z^14) + (2284179415871077852696767 I)/(2361183241434822606848 z^15) + O[1/z^16]) Zeta[I z + 1/2])/(4^((I z)/4) Pi^((I z)/2)) /; Abs[Arg[z^2]] < Pi && (Abs[z] -> Infinity)










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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