カム装置ってなんですか？？

大学数学、複素関数論、テータ関数に関する質問です。 写真のテータ関数の無限積表示（5.24）の式の1行目の形にどうやってしているのかと、命題5.22の（5.26）の証明を教えていただきたいです。

(b) テータ関数 ヤコビは楕円関数論の研究において, 次の級数を導入した。 9(2) = 22(-1)"-!g"-1/2)" sin(2n-1)Tu n=1 2(g/4 sin Tu-g/ sin 3Tu+q^/4 sin 5Tu-…). (5.23) 三 これはヤコビの楕円テータ関数(以下単にテータ関数(theta function))と呼 ばれるものの1つである. limd,(u)/2q'/4=Dsin Tu なので, 0,(u) は sin Tu 9→0 の一種の拡張と見ることができる。 伝統的な記号にならって, 以下 2ミe2miu a=2 q= eir, と書こう.gl<1だから Imr>0である. このとき(5.23)の右辺は TiT 2Tiu 9=e 9 2と(-1)"-1gm-1/2)?_2"-1/2 _2-n+1/2 =iこ(-1)"gm-1/2)°n-1/2 n=1 2i n=-00 = ig4z-1/2 (-1)"g"(n-1)z" n=-00 と書き直すことができる.右辺に3重積公式(5.22)を用いれば, テータ関数 の無限積表示が得られる: 0,(u) = iq'4z-1/2(1-2) II (1-g"2)(1-g"z-')(1-g") n=1. = 2q/4 sin Tu I (1-2g" cos 2Tu+g")(1-g"). 三 (5.24) n=1 命題5.22 0,(u) はuの整関数で 0,(-u) = ー6,(u). (5.25) 0 0(u) = 0 < (m,nEZ). 0,(u+1) = -0, (u), 9,(u+t) = -e-mi(r+2u)9, (u). (5.27) u= m+nT (5.26) 0 + 2u) [証明](5.25),(5.26) は(5.24)から簡単にわかる. また前節の無限積

英語の授業で日本の学校行事について話さなくてはいけないのですが全く出来ません(泣き 誰か文を考えてはくれないでしょうか？ 無理矢理ですいませんm(__)m どうかお願い致します

自分で解いたところ以外が分からないので教えてください！

N ンディ ーに 重証 Lesson (5 et's Practice! 1 次の語で、最も強く読む部分の記号を○で囲みましょう。 Finding My Future Lesson(5 (1) dair-y 5次の日本語に合うように,[ (1) 私は昨夜,テレビでドラマを見て楽しみました。 (2) re-al-ize ]内の語句を適切に並べかえましょう。 (3) de-liv-er-y ア(ィゥエ イ イウ (4) al-though (5) spe-cif-ic イウ I[watching / enjoyed / a drama] on TV last night. (6) ag-ri-cul-tur-al アィ(ゥエェオ ア ア on TV last night. (2) 錦織圭はテニスを練習することに注意を集中させました。 次の日本語を,指定された文字で始まる英語にしましょう。 Nishikori Kei focused [ tennis / practicing / on ]. health death ane (4) …にえさをやる feed (1) 健康 (2)価値 yalue Nishikori Kei focused (3) 死 (3) 早起きすることは私にとって難しい。 (5) プタ attend iving (6)…に立ち会う [early / getting/is/up]difficult for me. 上eS9ansihilty (7) 責任 (8) 生活 difficult for me. (4) 私の趣味は絵はがきを集めることです。 3( )内から適切な語句を選び,文を完成させましょう。 My[collecting /is/postcards /hobby]. (1) Jack likes 91ay ina (2) lenjoyed_5ee ing basketball.(plays / playing ) My a movie with my family. (to see / seeing ) (3) We learned about a letter in English.(to write /writing) 6次の英文の意味を書きましょう。 breakfast is important. (Eat / Eating) (1) I finished feeding the pigs. 私は( 4次の日本語に合うように, 空所に適切な語を入れましょう。 (2) Yui is interested in teaching English. (1) 私は皿を洗い終えました。。 結衣は( the dishes. (3) Taking pictures is interesting. (2) その生徒たちはウシの世話をすることを楽しんでいます。 )おもしろい。 (4) Ken is good at using computers. The students Care of cowWs. 健は( (3) 私の姉は海外で勉強することに興味があります。 My sister is interested abroad. 7次の日本語を英文にしましょう。 (4) 歌を歌うことは楽しい。 bno aevi! fun. (1) 私はその CD を聞いて楽しみました。 songs (5) 私の父の仕事は野菜を売ることです。 (2) ピアノを弾くことは簡単です。 Teum vegetables. My father's job aubl ey ai 43 42 四た SHOSEKI

書いてるところ以外がわからないので教えてください！

百五十 ンティ 盛に 9ロH ーに たド Lesson(5) Let's Practice! Finding My Future Lesson(5 1 次の語で、最も強く読む部分の記号を○で囲みましょう。 5次の日本語に合うように,[ (1)私は昨夜,テレビでドラマを見て楽しみました。 (1) dair-y ]内の語句を適切に並べかえましょう。 (2) re-al-ize (3) de-liv-er-y イ イウ ウエ (4) al-though I[watching / enjoyed / a drama] on TV last night. (5) spe-cif-ic (6) ag-ri-cul-tur-al アイ(ウ on TV last night. ア ア(イ ウ エオ (2) 錦織圭はテニスを練習することに注意を集中させました。 Nishikori Kei focused [ tennis/practicing / on ]. 2次の日本語を,指定された文字で始まる英語にしましょう。 218 Yalue death ane (4) .…にえさをやる feed (6)…に立ち会う attend ivina health (1) 健康 (2) 価値 Nishikori Kei focused (3) 死 (3) 早起きすることは私にとって難しい。 (5) プタ [early / getting/ is/up] difficult for me. FesPonsibilty difficult for me. (7) 責任 (8) 生活 (4) 私の趣味は絵はがきを集めることです。 3( )内から適切な語句を選び,文を完成させましょう。 My [collecting /is/postcards / hobby]. (1) Jack likes Play ina (2) lenjoyed_5ee ing basketball.(plays / playing) My a movie with my family.(to see / seeing) a letter in English. (to write/writing) 6次の英文の意味を書きましょう。 (3) We learned about (1) I finished feeding the pigs. wa breakfast is important. (Eat / Eating ) 過 私は( 現在 6 (2) Yui is interested in teaching English. 4次の日本語に合うように, 空所に適切な語を入れましょう。 結衣は( a (1) 私は皿を洗い終えました。 eitt (3) Taking pictures is interesting. the dishes. )おもしろい。 (2) その生徒たちはウシの世話をすることを楽しんでいます。 (4) Ken is good at using computers. care of cows. The students 健は( (3) 私の姉は海外で勉強することに興味があります。 abroad. My sister is interested 7次の日本語を英文にしましょう。 (4) 歌を歌うことは楽しい。 (1) 私はその CDを聞いて楽しみました。 o o antoeb bo cevil ert oop fun. songs (2) ピアノを弾くことは簡単です。 Ye taum vegetables. (5) 私の父の仕事は野菜を売ることです。 My father's job omino ofainow fnebote o 43 42 SHOSEKI

お願いします

3. The content on the Aspero Designs Web site is protected by copyright law and may not be reproduced - the company's written consent. 1. behind 2. without 3. except 4. before 4. Dr. Hemana and Dr. Wareham, the joint recipients of the Cobalt Research Prize, have known since they were university students in Auckland. 1. other one 2. another one 3. any other 4. each other 5. This afternoon's flights to Barcelona, London, and Rome have all been delayed inclement weather in the destination cities. 1.. as for 2. due to 3. now that 4. only if 6. Patrons who arrive at the theater the show has begun will not be seated until the intermission. 3. along 1. wherever 2. into 4. after 7. The new-product development meeting will be held either in Room 402 in Room 501. 1.. or 2. and 3. not 4. but 8. Printer cartridges can be found in the supply cabinet the file folders. 1.. at 2. from 3. with 4. along 9. Mr. Wong will travel to the management seminar in Singapore on 1.. he 2. himself 3. him 4. his own 10. Market researchers reported that customers were most impressed the Vestra Coffeemaker's delayed-start function. 1.. by 2. beyond 3. for 4. since After December 13 customers will be asked to place their orders online use the mail-order form. 1. So as 2. in case 3. rather than 4. provided that 12. its main competitor, the ergonomic chair offered by Well Designs is lightweight and comes in a variety of colors. 1. In contrast to 2. By way of 3. Instead of 4. So as

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1. The Milltown Cinema's outdoor cafe will be closed the winter months. 1. about 2. out of 3. next to 4. during 2. The department-wide changes suggested unanimous approval from company management. Ms.Juntasa received 1. in 2. of 3. by 4. as 3. The content on the Aspero Designs Web site is protected by copyright law and may not be reproduced - the company's written consent. 1. behind 2. without 3. except 4. before 4. Hemana and Dr. Wareham, the joint recipients of the Cobalt Research Prize, have known since they were university students in Auckland. 1. other one 2. another one 3. any other 4. each other 5. This afternoon's flights to Barcelona, London, and Rome have all been delayed inclement weather in the destination cities. 1. as for 2. due to 3. now that 4. only if 6. Patrons who arrive at the theater the show has begun will not be seated until the intermission. 1. wherever 2. into 3. along 4. after 7. The new-product development meeting will be held either in Room 402 in Room 501. 1. or 2. and 3. not 4. but 8. Printer cartridges can be found in the supply cabinet the file folders. 1. at 2. from 3. with 4. along 9. Mr. Wong will travel to the management seminar in Singapore on 1.. he 2. himself 3. him 4. his own 10. Market researchers reported that customers were most impressed delayed-start function. 1.. by the Vestra Coffeemaker's 2. beyond 3. for 4.. since

お願いします

6. Patrons who arrive at the theater 1.. wherever the show has begun will not be seated until the intermission. 2. into 3. along 4. after 7. The new-product development meeting will be held either in Room 402 in Room 501. 1. 2.. and 3. not 4. but or 8. the file folders. 4. along Printer cartridges can be found in the supply cabinet 1.. at 2. from 3. with 9. Mr. Wong will travel to the management seminar in Singapore on 1.. he 2. himself 3. him 4. his own 10. Market researchers reported that customers were most impressed delayed-start function. 1.. by - the Vestra Coffemaker's 2. beyond 3. for 4. since After December 13 customers will be asked to place their orders online -- use the mail-order form. 1.. so as 2. in case 3.rather than 4. provided that 12. ts main competitor, the ergonomic chair offered by Well Designs is lightweight and comes in a variety of colors. 1.. In contrast to 2. By way of 3. Instead of 4. So as 13. entering the main lobby. 3. Guests are asked to register at the front desk 1. upon 2. about in order to 4. whoever

お願いします

The Milltown Cinema's outdoor cafe will be closed the winter months. 1. about 2. out of 3. next to 4. during 2. The department-wide changes suggested Ms. Juntasa received unanimous approval from company management. 1. in 2. of 3. by 4. as 3. The content on the Aspero Designs Web site is protected by copyright law and may not be reproduced - the company's written consent. 1. behind 2. without 3. except 4. before 4. Dr. Hemana and Dr. Wareham, the joint recipients of the Cobalt Research Prize, have known since they were university students in Auckland. 1. other one 2. another one 3. any other 4. each other 5. This afternoon's flights to Barcelona, London, and Rome have all been delayed inclement weather in the destination cities. 1. as for 2. due to 3. now that 4. only if 6. Patrons who arrive at the theater the show has begun will not be seated until the intermission. 3. along 1. wherever 2. into after 7. The new-product development meeting will be held either in Room 402 in Room 501. 1.. or 2. and 3. not 4. but 8. Printer cartridges can be found in the supply cabinet the file folders. 1. at 2. from 3. with 4. along 9. Mr. Wong will travel to the management seminar in Singapore on 1.. he 2. himself 3. him 4. his own 10. Market researchers reported that customers were most impressed the Vestra Coffeemaker's delayed-start function. 1.. by 2. beyond 3. for 4. since

お願い

The Milltown Cinema's outdoor cafe will be closed the winter months. 1. about out of 3. next to 4. during 2. The department-wide changes suggested unanimous approval from company management. 1.. in Ms. Juntasa received 2. of 3. by 4. as 3. The content on the Aspero Designs Web site is protected by copyright law and may not be reproduced - the company's written consent. 1.. behind without 3. except 4. before 4. Dr. Hemana and Dr. Wareham, the joint recipients of the Cobalt Research Prize, have known since they were university students in Auckland. 1. other one 2. another one 3. any other 4. each other 5. This afternoon's flights to Barcelona, London, and Rome have all been delayed inclement weather in the destination cities. 1. as for 2. due to 3. now that 4. only if 6. Patrons who arrive at the theater the show has begun will not be seated until the intermission. 1.. wherever 2. into 3. along 4. after 7. The new-product development meeting will be held either in Room 402 in Room 501. 1.. or 2. and 3. not 4. but 8. Printer cartridges can be found in the supply cabinet the file folders. 3. 1. at 2. from with 4. along 9. Mr. Wong will travel to the management seminar in Singapore on 1.. he 2. himself 3. him 4. his own 10. Market researchers reported that customers were most impressed the Vestra Coffeemaker's delayed-start function. 1.. by 2. beyond 3. for 4. since After December 13 customers will be asked to place their orders online use the mail-order form. 1. so as 2. in case 3. rather than 4. provided that 12. its main competitor, the ergonomic chair offered by Well Designs is lightweight and comes in a variety of colors. 1.. In contrast to 2. By wayof 3. Instead of 4. So as