Leading Western analysts on East Germany have turned pessimistic about the economic prospects of that Communist country, long regarded as the East Bloc's best-managed nation.

Further, the East Berlin leadership now faces increasing strains with Western bankers over the financing of a debt that doubled in the past five years and, by the end of last year, had reached about the same per capita level as Poland's.

In view of the East German downturn, Western experts are voicing heightened concern about the country's continued refusal to disclose to creditors the kind of detailed economic and financial information provided lately by Polish and Romanian authorities.

A report issued this week by the West German Institute for Economic Research in Berlin, an authoritative observer of neighboring East Germany and one that has tended to be more optimistic about developments there than other Western institutes, concluded that East Germany's performance so far this year shows that the country has entered "a very difficult situation."

Official East German figures recently published for the first half of 1982 stated a growth of 3 percent in national income, well below the 4.8 percent target.

"Yes, you could say we have become more pessimistic," Manfred Melzer, an expert on East Germany at the Berlin institute, said in a telephone interview. "At the beginning of the year the economic situation didn't seem so bad."

In an effort to limit its Western debt, East Germany has slashed imports, causing shortages in some industrial supplies and fuels. Melzer and other Western experts say this is mainly responsible for crimping the country's production.

On top of that, the Soviet Union, on which East Germany depends for nearly all its oil, reportedly has cut back some oil shipments, forcing severe conservation measures on East German firms and a conversion of some power plants to lignite.

"They may have overdone forcing the firms to save," said Melzer, noting particularly that transport has been sharply curtailed by severe limits on the use of trucking fuel. "Industrial production has been slowed because factories haven't been able to get fuel and raw materials when needed."

But East German authorities have yet to admit lowering official growth targets in the current five-year plan. That plan, when approved a year ago, represented the only instance of an East Bloc country actually aiming for future targets higher than those in the 1976-80 planning period.

Instead, East German officials are quoted in the state-controlled press as exhorting the nation to buckle down and master the tougher economic challenges of the day. Much is said about meeting energy-saving targets and about progress -- despite a substantial drop in investment capital allowed under the current plan -- in installing robots and computer monitoring devices to improve industrial efficiency.

Such blinking of realities has not done much to bolster the confidence of Western bankers, and East Berlin reportedly is having trouble obtaining new Western credits or extending a large number of maturing ones.

The Berlin institute's report attributed this in part to the "crisis in confidence" over lending to East Bloc countries generally. This has developed with the rescheduling operations for the debts of Poland and Romania.

But other analysts complain that East Germany remains the most secretive of all the East Bloc states, refusing to divulge the kind of economic statistics that would make Western bankers more willing to advance new credits.

"They have the worst record of publishing statistics of any East Bloc country," declared Jan Vanous, editor of Wharton's Econometric Forecasting Associates in Washington. "It's not a reflection of their inability to generate the figures, but just a stubborn, uncooperative attitude. We don't know what the East Germans are really up to. I think they are hurting themselves this way."

The main public source of information on what East Germany owes to Western banks comes from the Bank for International Settlements (BIS) in Switzerland, which estimated the figure to be $9.2 billion at the end of March. This does not include a further $1.4 billion in credits from West Germany or additional sums from banks not reporting to BIS or from nonbanks or supplier credits.

The BIS figure showed a drop of $900 million in East German debt in the first quarter of this year, indicating attempts by East Berlin authorities to rid themselves of some financial exposure. But this was done by drawing down reserves, and Western analysts doubt the country has the resources to continue divesting this way at such a rate.

A large part of East Germany's debt comes due this year and next. BIS reported that about 40 percent of East Germany's total hard-currency bank debt at the end of 1981 consisted of obligations with a maturity period of less than one year.

Meantime, the share of hard-currency export revenues that East Berlin must apply to interest payments jumped from 9 percent five years ago to 24 percent at the start of this year.

Clearly, the pressure on East Germany to persuade Western banks to extend some credits is growing. An attempt to raise $350 million fell through in May. Vanous reported that East Germany has since approached some smaller U.S. banks about new loans, again indicating the difficulty East Berlin authorities are encountering with primary Western creditors.

Special relations with West Germany have assured the East Germans of some easing. In June the Bonn government agreed to extend another $340 million this year and $315 million next year in interest-free credits to finance trade between the two Germanies.

Both West Berlin's Institute for Economic Research and the Wharton service still regard East Germany as a relatively safe credit risk. "The conduct of East Germany shows no economic reasons which would speak out against the granting of subsquent credits," concluded the Berlin institute's report.

Said Vanous, noting East German efforts to reduce their debt: "They seem to be doing the right thing." But he also predicted "a showdown" between East Germany and Western bankers before long on the disclosure issue.