Higher Transcendental Functions, Volume 1McGraw-Hill, 1953 - Transcendental functions |
From inside the book
Results 1-3 of 88
Page 34
... obtain πs / 2г ( s / 2 ) ( ( s ) == · − ( 1 / s ) + 1 / ( s − 1 ) + √ ' w ( 1 / t ) t3 / 2 − 3 / 2 dt + - So w ( t ) 1 / 2-1 dt , and substituting 1 / t = t'in the first integral , we obtain ( 16 ) . For further integral ...
... obtain πs / 2г ( s / 2 ) ( ( s ) == · − ( 1 / s ) + 1 / ( s − 1 ) + √ ' w ( 1 / t ) t3 / 2 − 3 / 2 dt + - So w ( t ) 1 / 2-1 dt , and substituting 1 / t = t'in the first integral , we obtain ( 16 ) . For further integral ...
Page 47
... obtain the following asymptotic expansion ( Stirling series ) - ( 1 ) _log ( z ) = ( z – 1⁄2 ) log z −z + 1⁄2 log ( 2 ′′ ) - 2n- B2n / [ ( 2n − 1 ) ( 2n ) z2n − 1 ] + O ( z −2 −1 ) + n = 1 2n arg z < . This is equivalent to ( 2 ) г ...
... obtain the following asymptotic expansion ( Stirling series ) - ( 1 ) _log ( z ) = ( z – 1⁄2 ) log z −z + 1⁄2 log ( 2 ′′ ) - 2n- B2n / [ ( 2n − 1 ) ( 2n ) z2n − 1 ] + O ( z −2 −1 ) + n = 1 2n arg z < . This is equivalent to ( 2 ) г ...
Page 79
... obtain a large number of integral formulas . Starting , e.g. , with 2.1 ( 15 ) , substituting z for z , and applying Mellin's transformation formula , we obtain - г ( a + s ) ( 4 ) г ( a ) I ( b + s ) I ( c ) Г ( b ) r ( c + s ) I ...
... obtain a large number of integral formulas . Starting , e.g. , with 2.1 ( 15 ) , substituting z for z , and applying Mellin's transformation formula , we obtain - г ( a + s ) ( 4 ) г ( a ) I ( b + s ) I ( c ) Г ( b ) r ( c + s ) I ...
Contents
FOREWORD | xxiv |
2 | xxvi |
Expressions for some infinite products in terms | 5 |
Copyright | |
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½µ according analytic continuation applying assume asymptotic B₂ Chapter circle coefficients complete confluent connected consider constant contour converges cosh defined definition denotes derived differential equation easily equal Erdélyi Euler's expansions expression F a,b follows formula gamma Gauss given gives Hence hypergeometric equation hypergeometric functions hypergeometric series indented independent integral representations integrand linear London loop Math means multiplication notation numbers obtain parameters points poles polynomials positive Proc proved Read real axis REFERENCES relations replaced residues respectively Riemann's right-hand side satisfies shown singularities sinh solutions substitution term theorem theory tion transformation valid values variable zero