My first Contribution to this forum. One year later Q 98831


Question and Answers Forum

All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
Question Number 143698 by Dwaipayan Shikari last updated on 17/Jun/21

$M y f i r s t C o n t r i b u t i o n t o t h i s f o r u m .$ $O n e y e a r l a t e r$ $Q 98831$
Commented by Dwaipayan Shikari last updated on 17/Jun/21

$M a d Q u e s t i o n o n t h a t s a m e d a y . M r . M J S s a i d t h a t i t$ $C o n s i s t s H y p e r g e o m e t r i c f u n c t i o n . I {d i d n}^{'} t k n o w$ $A b o u t H y p e r g e o m e t r i c f u n c t i o n s$ $Q 98951$
Commented by Dwaipayan Shikari last updated on 17/Jun/21

$A n o t h e r M a d Q u e s t i o n!$ $Q 98929$
Commented by Dwaipayan Shikari last updated on 17/Jun/21

$\int {t a n}^{\frac{1}{5}} (x) c o t (x) s e c (x) d x$ $= \int \frac{{s i n}^{- 4 / 5} x}{{c o s}^{1 / 5} x} d x s i n x = t$ $= \int t^{- 4 / 5} {(1 - t^{2})}^{- 3 / 5} d t$ $= \underset{n = 0}{\sum^{\infty}} \frac{{(\frac{3}{5})}_{n}}{n!} \int t^{- 4 / 5} t^{2 n} d t = \underset{n = 0}{\sum^{\infty}} \frac{{(\frac{3}{5})}_{n}}{n!} . \frac{1}{2 n + \frac{1}{5}} t^{2 n + \frac{4}{5}} + C$ $= \frac{t^{1 / 5}}{2} \underset{n = 0}{\sum^{\infty}} \frac{{(\frac{3}{5})}_{n}}{n! (n + \frac{1}{10})} t^{2 n} + C$ $= \frac{t^{1 / 5}}{2} \underset{n = 0}{\sum^{\infty}} \frac{{(\frac{3}{5})}_{n} Γ (n + \frac{1}{10})}{n! Γ (n + \frac{11}{10})} t^{2 n} = 5 \sqrt[5]{t} \underset{n = 0}{\sum^{\infty}} \frac{{(\frac{3}{5})}_{n} {(\frac{1}{10})}_{n}}{n! {(\frac{11}{10})}_{n}} t^{2 n} + C$ $= 5 \sqrt[5]{t}_{2} F_{1} (\frac{3}{5}, \frac{1}{10} ∣ \frac{11}{10}, t^{2}) + C$ $= 5 \sqrt[5]{s i n (x)}_{2} F_{1} (\frac{3}{5}, \frac{1}{10} ∣ \frac{11}{10}; {s i n}^{2} x) + C$
Commented by Ar Brandon last updated on 17/Jun/21

$Happy Birthday on this forum . Haha! In one$ $year I think {you}^{'} ve progressed a lot . Thanks$ $for your teachings, Sir .$ 😉
Commented by Dwaipayan Shikari last updated on 17/Jun/21

$H a h a h a h a Y o u n g B o y s . B u t i h a v e$ $t u r n e d m y s e l f i n t o a C a t .$ $I w a s a B l a c k h o l e . I t w i l l$ $t a k e a n o t h e r y e a r t o b e c o m e a$ $M a n$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum