Download E-books Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas PDF

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By Yury A. Brychkov

Due to the quite a few purposes fascinated with this box, the speculation of distinct services is below everlasting improvement, particularly concerning the specifications for contemporary machine algebra tools. The instruction manual of distinct capabilities presents in-depth insurance of specific capabilities, that are used to aid resolve the various so much tough difficulties in physics, engineering, and arithmetic. The booklet offers new effects in addition to recognized formulation utilized in a few of the most crucial mathematical equipment with the intention to clear up a large choice of difficulties. It additionally discusses formulation of connection and conversion for undemanding and targeted services, similar to hypergeometric and Meijer G features.

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Eleven. ✂✁❊❉✣✟ ✲✷✶✠✓ ✡✔✝✵❢✾✡ ✸❤✟✫☞ ✁  ✂✁❊❉✣✟ ✁✫✲✷✶✠✓ ✡ ✡ ✟ ♠ ✭ ✜ ✤ ❍❖❍ ✂ ➔ ✝ ↔✡➁ ☞ ✎ ✸ ♠ ✕ ✁ ✟ ✲❀✁✫✲✷✶ ✡ ✟ ✱ ✮ ♠ ✺ ✜ ✤ ➔ ✜✣✢✌✂✬✛✬ ✦ ✪ ♠ ✺ ✜ ✤ ↕ ❛ 12. ✁ ❉✣✟ ✁ ✶✠✓ ✡ ✝✵❢ ✡ ✸❤✟✫☞ ✁   ✁ ❉✣✟ ✲✷✶✠✓ ✡ ✡ ✟ ♠ ✭ ✜ ✤ ❍❖❍ ✢ ✡✟ ♠ ✭ ✜ ✤ ♠ ✺ ✜ ✤ ❛ ✡ ✡ ✡ ✡ thirteen. ✂✁❊❉✣✟ ✁ ✶✠✓  €✁❊❉✣✟ ✲✷✶✠✓ ✝✵❢ ✸❤✟✫☞ ✁✫✲✷✶✠✓ ✡ ✟ ♠ ✭ ✜ ✤ ❍❖❍ ➔ ✝✹✸ ➣ ☞ ✁ ❋ ✢✼ ● ✡ ❢ ✡ ✁ ✝✠❢ ✡ ✸❤✟✫☞ ✲❀✁✫✲✷✶✠✓ ✡ ✡ ✟ ✁ ♠ ✺ ✜ ✤ 14. ✂✁❊❉✣✟ ✁✫✲✷✶✠✓ ✡  €✁❊❉✠✝✠❢ ✡ ✸❤✟✫☞ ✁✫✲✷✶✠✓ ✡ ✡ ✟ ♠ ✭ ✜ ✤ ❍❖❍ ➔ ✝✹✸ ➣ ☞ ✁ ❋ ✢✼ ● ✡ ❢ ✡ ✁ ✟ ✲✷✶✠✓ ✡ ✝✠❢ ✡ ✸❤✟✫☞ ✲❀✁✫✲✷✶✠✓ ✡ ✡ ✟ ✁ ➣ ➣ ➀ ➔ → 15. ✂✁☎✄ ✟ ✁✫✲✷✶ ✝ ✸❤❢■✟✫☞ ✁  ✂✁☎✄ ✡ ✟ ✝ ✸❤❢■✟✫☞✵✍ ✍ ➣ ➣ ➔➀→ sixteen. ✁ ✄ ✝ ✸❤❢■✟✫☞ ✁   ✁ ✄ ✟ ✁✫✲✷✶ ✡ ✟ ✝ ✸❤❢■✟✫☞✵✍ ✍ ➣ ➣ ❛ ➣ 17. ✂✁☎✄ ✟ ✁ ✶ ✝ ✸❤❢■✟☛☞ ✲✷✶  ✂✁☎✄ ✟ ✲✷✶ ✝ ✸❤❢■✟☛☞ ✁ ✡ ✟ ✝ ✸❤❢■✟✫☞✠✍ ✍ ➔ ✝✹✸ ➣ ☞ ✁ ✝ ➁ ✎ ☞ ✡ ❢ ✁ ✝ ➣ ✸❤❢■✟✫☞ ✲❀✁✫✲✷✶ ✡ ✟ ➣ ➔ ✝ ➁ ✎ ☞✹✡✌❢ ✁ ✡ ✟ ✝ ➣ ✸❤❢■✟✫☞ ↕ ❛ ➣ 18. ✂✁☎✄ ✟ ✁ ✶ ✝ ✸❤❢■✟☛☞ ✁  ✂✁☎✄ ✟ ✲✷✶ ✡ ✟ ✝ ✸❤❢■✟✫☞✵✍ ✍ 6. ✡ ✁ ❛ ✶❀❉☛✡ ✟ ♠ ✺  ✂✁ ❉ ✡ ✟ ♠ ✭ ➔ 1. 1. 7. Inverse trigonometric capabilities 1. ❂ ✬✯❃❄✼❘❅❈❇ ❂ ✬✯❃❄✼❘❅❈❇ ❂ ✬✽❃❄✼❆❅❈❇ ❂ ✬✽❃❄✼❆❅❈❇ ♠ ✺ ✜ ✤ ↕ ♠ ✭ ✜ ✤ ♠ ✺ ✜ ✤ ↕ ♠ ✭ ✜ ✤ ♠ ✺ ✜ ✤ ↕ ♠ ✭ ✜ ✤ ❂ ✬✽❃❄✼❆❅❈❇ ❂ ✬✽❃❄✼❆❅❈❇ ✝ ➣ ✸❤❢■✟✫☞ ↕ ✝♠ ✤  ✂✁☎✄ ✠☛✡✄☞ ☎ ✝ ✟ ✝✠❢■✟✫☞✵✍ ➔ ✝✖✸✂✁❆☞ ✁✫✲✷✶ ✝ ➁ ✸ ➣ ☞ ✎ ❢ ✁ ✝ ➣ ❤ ✸ ❢✾✡✌✟☛✡✌☞ ✲❀✁✔✓ ✡ ❥ ✁✫✲✷✶ ❋ ✜ ✼✏✭ ♠ ✂ ✤ ✂ ● ✬ ❃❄✼❘❅❈❇ ❂✯ ✚✙✸  ✁ ✄✂✆☎✝✂✟✞✠ ✟✞☛✡ ✞✌☞✟✍ ✎✑✏ ✆✟✍ ✎ ✞✠✡ 2. three. four. five. 6. 7. ✂✁☎✄ ✠☛✡✄☞✌☞✌✍ ☎ ✵✝ ❢■✟✫☞✠✍ ✝♠ ✤ ➔ ✝✖✸ ➣ ☞ ✁ ✁ ✁✫✲✷✶ ✝ ➁ ✸ ➣ ☞ ✎ ❢ ✁ ✝ ➣ ❤ ✸ ❢✾✡✌✟☛✡✌☞ ✲❀✁✔✓ ✡ ❥ ✫✁ ✲✷✶ ❋ ✜ ✼ ✭ ♠ ✂ ✤ ✂   ✡ ✁☎✄ ✠☛✡✄☞ ✎ ✠ ✟ ✝✠❢■✟✫☞✵✍ ✼ ➔ ✝✹✸ ➣ ☞ ✁ ✝ ↔✖➁ ✸ ➣ ☞ ✎ ❢✾✡ ✁ ❛ ✶ ✟❀✝ ➣ ✓ ❢✾✡❖✟☛✡✌☞ ✲❀✁✫✲✷✶✠✓ ✡ ✏ ✡ ✁✫✲✷✶ ❋ ✜ ✼❁✺ ♠ ✂ ✤ ✂   ✡ ✁ ❛ ✶✥✄ ✠☛✡✄☞ ✎ ✠ ✟ ✝✠❢■✟✫☞✵✍ ➔ ✝✹✸ ➣ ☞ ✁ ✝ ↔✖➁ ☞ ✎ ❢✾✡ ✁ ❛ ✶ ✝ ➣ ✓ ❢✾✡❖✟☛✡✌☞ ✲❀✁✫✲✷✶✠✓ ✡ ✣ ❛ ❋ ✡✁ ✶ ✜   ✡ ✁☎✄ ✠☛✡✄☞✌☞✌✍✏✎ ✝✠❢■✟✫☞✵✍ ✼ ➔ ✝✹✸ ➣ ☞ ✁ ❛ ✶ ✝ ↔✖➁ ✸ ➣ ☞ ✎ ❢✾✡ ✁ ❛ ✶ ✟❀✝ ➣ ✓ ❢✾✡❖✟☛✡✌☞ ✲❀✁✫✲✷✶✠✓ ✡ ✏ ❋ ✡ ✁✫✲✷✶ ✜ ✼❁✺ ♠ ✂ ✤ ✂   ✡ ✁ ❛ ✶✥✄ ✠☛✡✄☞✌☞✌✍✏✎ ✝✠❢■✟✫☞✵✍ ➔ ✝✹✸ ➣ ☞ ✁ ❛ ✶ ✝ ↔✖➁ ☞ ✎ ❢✾✡ ✁ ❛ ✶ ✝ ➣ ✓ ❢✾✡❖✟☛✡✌☞ ✲❀✁✫✲✷✶✠✓ ✡ ✣ ❛ ❋ ✡✁ ✶ ✜  ✂✁☎✄ ✠☛✡✄☞ ☎ ✝ ✟ ✜✠✭ ✝✠❢❀✦ ✴ ✬❪✧ ✟✞  ☞✵✍ ✼✏✭ ✢ ♠ ✂ ✤ ✝ ➔ ➁ ➣ ✎ ✢ ✝ ✸ ☞ ❢ ✁ ✝✵✟◗✸❤❢ ✡ ✟ ✡ ☞ ✲❀✁✔✓ ✡ ❥ ✁✫✲✷✶ ✢ ♠ ✜ ♠ ✂ ✤ ✂ ✭✽✤ ✮ ✒ ✚✠☛ ✚✠☛ ❁ ● ❂ ✬✯❃❄✼❘❅❈❇ ● ❂ ✬✯❃❄✼❘❅❈❇ ✼ ↕ ✼❁✺ ♠ ✂ ✤ ✂ ● ❂ ✬✯❃❤✼❆❅❈❇ ● ✼ ↕ ✼❁✺ ♠ ✂ ✤ ✂ ● ✱  ✂✁☎✄ ✠☛✡✄☞ ✎ ✠ ✟ ✠✝ ❢❀✴ ✣✜ ✬✮ ✟✞☞✵✭✿✍ ✼❳✦ ✪ ✳ ➔ ✢ ❢■✟ ✠✶ ✓ ✡ ✲❀✁ ✝✠❢ ✡ ✟✩✓ ➣ ☞ ✲❀✁ ❥ ✰ ✶✠✓ ✡ ✲❀✁✾❧❈✲❀✁ ✝ ↔ ❢ ✡ ✟☛✓ ➣ ☞ ✁✫✲✷✶ ♠ nine. ✂✁❊❉▼✟ ✁✫✲✷✶ ✠☛✡✄☞ ☎ ✝ ✟ ✜ ✤ ❍ ✬★✧   ✤✂✭ ✢ ♠ ✂ ➔ ✸ ✝ ✢ ✝ ➁ ✸ ➣ ☞ ✎ ❢ ✁ ✟ ✲✷✶ ✝✵✟◗✸❤❢✾✡✌☞ ✲❀✁✔✓ ✡ ❥ ✂ ✁✫✲✷✶ ✮ ✢ ♠ ✜ ♠ ✭✽✤ ✱ ♠ 10. ✁ ❉✣✟ ✁✫✲✷✶ ✠☛✡✄☞ ✎ ✠ ✟ ✜ ✤ ❍ ✂ ✬ ➔ ✜✠✭ ✢ ✼✒✦ ✝ ➁ ✸ ➣ ☞ ✎ ❢■✟ ✁✫✲✦✫✹✓ ✡ ✝✵✟☛✓ ❢ ✡ ☞ ✲❀✁ ❥ ✰ ✶✠✓ ✡ ✲❀✁✾❧❈✲❀✁ ✳ ✢ ✤♠ ✓ ➣ ✱ ✮ ✁✫✲✷✶ ➣ ➣ ❛ eleven. ✁ ✑❦✟ ✁✫✲✷✶✠✓ ✡ ✝ ✸❤❢ ✡ ✟✫☞ ✁ ✶✠✓ ✡   ✁ ✑▼✝ ✸❤❢ ✡ ✟✫☞ ✲✷✶✠✓ ✡ ✠☛✡✄☞ ☎ ✝ ✟ ✝✠❢❀✴ ✟✞☞ ✘✞✘ ➔ ❋ ✢✼ ● ✡ ❢✾✡ ✁ ✟ ✲✷✶✠✓ ✡ ✠ ✡✄☞ ☎✞✝ ✟ ✁ ➣ ❛ 12. ✂✁✒✑❦✟ ✁ ✶✠✓ ✡✔✝ ✸❤❢✾✡✌✟✫☞ ✁✫✲✷✶✠✓ ✡☎ ✂✁✒✑❦✟ ✲✷✶✠✓ ✡ ✠ ✡✄☞ ☎✞✝ ✟ ✝✵❢❀✴ ✟✞☞ ✘ ✘ ➔ ❋ ✢✷✼ ● ✡ ❢✾✡ ✁ ✝ ➣ ✸❤❢✾✡❖✟✫☞ ✲✷✶✠✓ ✡ ✠ ✡✄☞ ☎✞✝ ✟ ✁ ✁ ✑❦✟ ✲✷✶✠✓ ✡✔✝ ➣ ✸❤❢✾✡✌✟✫☞ ✁ ❛ ✶✠✓ ✡☎ ✂✒✁ ✑❦✟ ✁✫✲✷✶✠✓ ✡✔✝ ➣ ✸❤❢✾✡✌✟✫☞ ✲✷✶✠✓ ✡ ✠ ✡✄☞ ☎✞✝ ✟ ✝✠❢ ✴ ✟ ☞ ✘ ✘ thirteen. ✂✒ ➔ ✝✹✸✝ ❱☞ ✲❀✁ ✝ ↔✡➁ ☞ ✎ ✟ ✲❀✁✫✲✷✶ ✠ ✡✄☞ ☎✞✝ ✟ eight. ✚✝✺ ❂ ✬✯❃❄✼❘❅❈❇ ❂ ✬✯❃❄✼❘❅❈❇ ❂ ✬✯❃❄✼❘❅❈❇ ❂ ✬✯❃❄✼❘❅❈❇ ✝✠❢❀✴ ✟✞☞ ↕ ✝✵❢ ✴ ✟✞☞ ↕ ✝✵❢❀✴ ✟✞☞ ↕ ☎✝✂  ✟✂✗✞✁  ✞✁  ✗☞ ☞✄✂ ✍ ✆✆☎✞✝ ✞ ✆✑✏☛✡✌☞ ✄✎✍ ✆✟✍ ✁☎✄  ✆✝✏✎✏☛☞✞✒✠ ☎✝✂  ✟✂  ✂✁ 14.

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